CAIMS 2018June 4-7, 2018, Ryerson University, Toronto, Ontario, Canada

Scientific Theme: Computational Mathematics and ApplicationsOrganizer: Katrin Rohlf, Ryerson University, Canada

Plenary Speaker: Linda Petzold, UC Santa Barbara, USA

Minisymposium: Recent Advances in Scientific ComputingOrganizers: Bamdad Hosseini, California Institute of Technology,

USA; John Stockie, Simon Fraser University, Canada; PaulTupper, Simon Fraser University, Canada

Contributed Talks: Scientific Computing

List of abstracts

A well-balanced meshless tsunami propagation and inundationmodelBihlo, Alex (Memorial University of Newfoundland, Canada) . . . . . . . . . . . . . . . . . . . . . 5

Accuracy Analysis of Hybrid Stochastic Simulation Algorithms

Cao, Young (Yang) (Virginia Tech, USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Towards new high-order operator-splitting time-integration meth-odsCervi, Jessica (University of Saskatchewan, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

Algebraic Linearizations of Matrix Polynomials

Chan, Eunice (University of Western Ontario, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

An overdetermined eigenvalue problem in linear elasticity

Dominguez, Sebastian (Simon Fraser University, Canada) . . . . . . . . . . . . . . . . . . . . . . . . 6

Visualizing fractal patterns in DNA sequences using chaos gamerepresentationDo Pham, Martin (University of Waterloo, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Rule-based modeling of biochemical systems

Faeder, James (University of Pittsburgh, USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Numerical methods for the microscopic cardiac electrophysiologymodelFokoue, Diane (University of Ottawa, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Model reduction of Stochastic Models of Biochemical Systems

Gholami, Samaneh (Ryerson University, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Extended BACOLI: Solving one-dimensional multi-scale parabolicPDE systems with error controlGreen, Kevin (University of Saskatchewan, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Meshfree finite difference methods for fully nonlinear elliptic equa-tionsHamfeldt, Brittany (New Jersey Institute of Technology, USA) . . . . . . . . . . . . . . . . . . . 9

Parallel iterations for nonlinear boundary value problems

Haynes, Ronald (Memorial University, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Function space MCMC for posteriors with non-Gaussian priors

Hosseini, Bamdad (California Institute of Technology, USA) . . . . . . . . . . . . . . . . . . . . . 10

Efficient Computation of Breaking Points in State-Dependent De-lay Differential EquationsHumphries, Tony (McGill University, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

An effective hybrid strategy for stochastic reaction-diffusion bio-chemical systems with delayIlie, Silvana (Ryerson University, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Synthetic biology approaches to suppression of antibiotic resis-tance: toward model-based designIngalls, Brian (University of Waterloo, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

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Hybrizidable Discontinuous Galerkin Method for Linear Free Sur-face ProblemsJones, Giselle Sosa (University of Waterloo, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

An Eulerian droplet model: Mathematical analysis and improve-mentKeita, Sana (University of Ottawa, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

Error Analysis of a Space-Time Hybridizable DiscontinuousGalerkin Method for the Advection-Diffusion EquationKirk, Keegan (University of Waterloo, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

A Fast Integral Equation Method for the Navier-Stokes Equationsin 2DKlinteberg, Ludvig af (Simon Fraser University, Canada) . . . . . . . . . . . . . . . . . . . . . . . . 12

Solving heat equation via a combined method of CPM and RBF

Lun, Chu Alex Shiu (University of British Columbia, Canada) . . . . . . . . . . . . . . . . . . .13

Preconditioned Iterative techniques for geophysical electromag-netic problemsMacLachlan, Scott (Memorial University of Newfoundland, Canada) . . . . . . . . . . . . 13

Recent Advances in Gaussian Collocation Software for BoundaryValue ODEs and 1D PDEsMuir, Paul (Saint Mary’s University, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

A class of 2D coupled bulk-surface reaction-diffusion models andtheir bifurcation analysisPaquin-Lefebvre, Frederic (University of British Columbia, Canada) . . . . . . . . . . . . . 14

Cell Polarization and Growth in Yeast Mating

Petzold, Linda (University of California Santa Barbara, USA) . . . . . . . . . . . . . . . . . . . 15

Weakly compressible flow through a cylinder with density-dependent viscosity and Navier-slip at the wallRohlf, Katrin (Ryerson University, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Arbitrary order A-stable methods for Ordinary differential Equa-tions via deffered correctionSaint-Cyr, Koyaguerebo-Ime (University of Ottawa, Canada) . . . . . . . . . . . . . . . . . . . . 16

Multi-Particle Collision Dynamics for Modeling Reaction-DiffusionSystemsSayyidmousavi, Alireza (Ryerson University, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Microscopic Models of Synthetic Nanomotors

Schofield, Jeremy (University of Toronto, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Elliptic PDEs on composite domains via the Schwarz alternatingmethod and the Closest Point MethodShao, Aili (University of British Columbia, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

A spectral method for nonlocal diffusion operators on the sphere

Slevinsky, Richard Mikael (University of Manitoba, Canada) . . . . . . . . . . . . . . . . . . . . 17

High-Order Operator-Splitting Methods for the Bidomain andMonodomain ModelsSpiteri, Raymond (University of Saskatchewan, Canada) . . . . . . . . . . . . . . . . . . . . . . . . 18

Controlling diffusion in Reactive Multiparticle Collision Dynamics

Strehl, Robert (Industry, Germany) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

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Resilience of network synchronization against structural and dy-namical perturbationsSun, Jie (Clarkson University, USA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Fitting a Stochastic Model to Eye Movement Time Series

Tupper, Paul (Simon Fraser University, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Numerical Method for Solving Optimal Mass Transport arisingfrom Image RegistrationWan, Justin (University of Waterloo, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

A numerical method for solving ODEs on surfaces

Wong, Tony (University of British Columbia, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . 20

An Hermite-Obreschkoff Method for Stiff High-Index DAEs

Zolfaghari, Reza (McMaster University, Canada) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

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Abstracts

A well-balanced meshless tsunami propagation andinundation modelBihlo, Alex (abihlo@mun.ca)Memorial University of Newfoundland, St. John’s, Canada

A well-balanced radial basis function based finite difference (RBF-FD) discretiza-tion of the shallow-water equations is developed, serving as the core of a meshlesstsunami propagation and inundation model. Well-balancedness requires the preser-vation of the lake-at-rest solution of the shallow-water equations over arbitrary bot-tom topography. We present a universal criterion guaranteeing well-balancedness ingeneral mesh-based and meshless numerical schemes. This is achieved by a specificmimetic design of the spatial derivative operators in the momentum flux equations ofthe shallow-water equations.

Based on this well-balanced RBF-FD discretization of the shallow-water equa-tions, we develop a meshless tsunami propagation and inundation model. The mov-ing shoreline boundary condition required for the inundation model is handled usingcompactly supported RBF extrapolation. The resulting inundation models is thustruly meshless. Numerical results are presented to showcase the excellent agreementof the proposed model with standard one- and two-dimensional benchmark tests.

This is joint work with Rudiger Brecht, Scott MacLachlan (Memorial Universityof Newfoundland) and Jorn Behrens (University of Hamburg).

Accuracy Analysis of Hybrid Stochastic SimulationAlgorithmsCao, Young (Yang) (ycao@cs.vt.edu)Virginia Tech, Blacksburg, USA

Noise in cellular systems is often modeled and simulated with Gillespie’s stochasticsimulation algorithm (SSA), but the low efficiency of the SSA limits its applicationto large biochemical networks. To improve the efficiency of stochastic simulations,Haseltine and Rawlings (HR) proposed a hybrid algorithm, which combines ordinarydifferential equations (ODEs) or partial differential equations (PDEs) for traditionaldeterministic models and the SSA for stochastic models. In this work, we present asystematic way to study the accuracy of approximation methods such as slow-scaleSSA (ssSSA) or the HR hybrid method. Mathematical analysis and numerical resultsboth show that the HR hybrid method is accurate if either the quantity of reactantmolecules in fast reactions is above a certain threshold, or the reaction rates of fastreactions are much larger than those of slow reactions. This analysis also shows thatthe HR hybrid method approximates the chemical master equation (CME) well for amuch greater region in system parameter space than the slow-scale SSA (ssSSA) andthe stochastic quasi-steady-state assumption (SQSSA) methods.

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Towards new high-order operator-splitting time-integrationmethodsCervi, Jessica (jessica.cervi@usask.ca)University of Saskatchewan, Saskatoon, Canada

The bidomain and monodomain models are among the most widely used math-ematical models to describe cardiac electrophysiology. Because the systems of dif-ferential equations associated with these models are large and strongly non-linear,numerical solutions to these systems are often found via operator-splitting methods.In this talk, we will focus on splitting methods with order higher than two that,according to the ShengSuzuki theorem and the theory developed by Goldman andKaper, require backward time integration and historically have been considered un-stable for solving deterministic parabolic systems. We demonstrate the accuracy andgains in efficiency of higher-order operator-splitting methods to solve several prob-lems arising in the field of car-diovascular modeling. Finally, we present preliminaryresults regarding the stability analysis of operator-splitting methods.

Algebraic Linearizations of Matrix PolynomialsChan, Eunice (echan295@uwo.ca)University of Western Ontario, London, Canada

We show how to construct linearizations of matrix polynomials za(z)d0 + c0,a(z)b(z), a(z) + b(z) (when deg (b(z)) < deg (a(z))), and za(z)d0b(z) + c0 fromlinearizations of the component parts, a(z) and b(z). This allows the extension tomatrix polynomials of a new companion matrix construction.

An overdetermined eigenvalue problem in linear elas-ticityDominguez, Sebastian (domingue@sfu.ca)Simon Fraser University, Vancouver, Canada

Properties regarding the Lame operator have been deeply studied in the pastcentury as more applications involving linear elastic materials arise. One interest-ing application is the fluid-solid interaction problem. In particular, the coupling ofisotropic and bounded materials with unbounded compressible and inviscid fluids isan application of recent interest. It is known that the time harmonic regime of thisproblem possesses a non-trivial kernel. The functions in this kernel are called Joneseigenfunctions. These eigenfunctions satisfy an overdetermined eigenvalue problem,which in this case implies that the spectrum of this problem is intimately related tothe shape of the domain. We provide existence of eigenpairs in Lipschitz domains andnumerical approximations via the finite element method.

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Visualizing fractal patterns in DNA sequences usingchaos game representationDo Pham, Martin (martindopham@gmail.com)University of Waterloo, Waterloo, Canada

The Canadian government’s decision to legalize cannabis in 2018 presents an op-portunity for further research in the cultivation and medical application of the plant.Cannabis is a psychoactive drug that is commonly consumed worldwide, with a his-tory of usage dating back thousands of years. Recently, the DNA sequencing forover 1000 strains of cannabis was made publicly available. This talk will present afractal-based analysis of the chaos game representation of four cannabis sativa strainsfrom different regions around the world. Fractals are objects with a high degree ofself-similarity and scale-invariant complexity. Chaos game representation (CGR) isa method first proposed by HJ Jeffrey (1990) to represent gene structure, display-ing local and global patterns. The chaos game on iterated function systems will beintroduced as a method for generating fractals, followed by a discussion of fractal di-mension as a scaling relationship between length and area. Numerical approximationsof the fractal dimension of cannabis CGR will then be presented, as well as next stepstowards multifractal analysis.

Rule-based modeling of biochemical systemsFaeder, James (faeder@pitt.edu)University of Pittsburgh, Pittsburgh, USA

The rule-based modeling (RBM) approach, in which biological molecules can berepresented as structured objects whose interactions are governed by rules that de-scribe their biochemical interactions, is the basis for addressing multiple scaling issuesthat arise in the development of large scale models.

Although simpler coarse-grained models are often useful for gaining insight intobiological mechanisms, such detailed models are necessary to understand how molec-ular components work in the network context and essential to developing the abilityto manipulate such networks for practical benefits. Currently available software toolsfor RBM, such as BioNetGen, Kappa, and Simmune, enable the specification andsimulation of large scale models, and these tools are in widespread use by the mod-eling community. I will review some of the methodological developments that gaverise to those capabilities, such as the development of rule-based languages and thenetwork-free simulation method, and then I will describe ongoing efforts to visual-ize complex models, to improve the underlying simulation algorithms, to developspatially-resolved models, and the develop efficient methods for calibrating models toexperimental data.

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Numerical methods for the microscopic cardiac elec-trophysiology modelFokoue, Diane (dfoko042@uottawa.ca)University of Ottawa, Ottawa, Canada

Several mathematical models are available for the simulation of the cardiac electri-cal activity at various scales. For instance, the bidomain model represents the cardiacaction potential at the organ level. For studying propagation between a smaller groupof myocytes, the microscopic model is based on an explicit representation of individ-ual cells. At the microscopic level, the cardiac tissue can be viewed as two separatedomains: the intra-cellular and extra-cellular domains, respectively Ωi and Ωe sepa-rated by cellular membranes Γ. The microscopic model consists in a set of Poissonequations, one for each sub-domain Ωi and Ωe, coupled on interfaces Γ with nonlineartransmission conditions involving a system of ODEs. Few numerical methods havebeen proposed in the literature for the microscopic model.

In this talk, we focus on the numerical solution of the microscopic model. Anoperator splitting method is used at each time step to solve two separate problems,namely the nonlinear ODE models representing the ionic activity on Γ and coupledlinear space propagation problems on Ωi and Ωe. To handle the non-standard trans-mission conditions coupling the solutions on Ωi and Ωe, we propose a non-overlappingdomain decomposition (DD) method. Our talk addresses convergence issues of thisDD method and presents numerical results for the microscopic models. Co-author:Yves Bourgault.

Model reduction of Stochastic Models of BiochemicalSystemsGholami, Samaneh (samaneh.gholami@ryerson.ca)Ryerson University, Toronto, Canada

Stochastic modelling and simulation of biochemical reaction networks have be-come very popular in recent years. Biochemical systems have important practicalapplications, in particular to understanding critical intra-cellular processes. The dy-namics of cellular systems involving some small molecular amounts of certain speciesis accurately described using stochastic models. Stochastic cellular behaviours areoften modelled using the formalism of jump Markov processes, whose probabilitydistributions evolve according to the chemical master equation (CME). These mod-els typically depend on a set of kinetic parameters whose values are not accuratelymeasured.

Model reduction techniques for deterministic continuous models of biochemicalnetworks were developed in the literature, however much less research exists on modelreduction of stochastic discrete biochemical kinetics. We propose a model reductionscheme for the CME, based on sensitivity analysis. This approach is successfully ap-plied on some biochemical models of practical interest. The behaviour of the reducedsystem matches well that of the full system. Moreover, the reduced system is easierto analyze and faster to simulate.

This is joint work with S. Ilie.

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Extended BACOLI: Solving one-dimensional multi-scale parabolic PDE systems with error controlGreen, Kevin (kevin.green@usask.ca)University of Saskatchewan, Saskatoon, Canada

BACOLI is a Fortran software package for solving one-dimensional parabolic par-tial differential equations (PDEs) with separated boundary conditions by B-splineadaptive collocation methods. A distinguishing feature of BACOLI is its ability toestimate and control error as well as correspondingly adapt meshes in both space andtime.

Many models of scientific interest, such as those that arise in cardiac electro-physiology for example, require the coupling of systems of parabolic PDEs describingdiffusive transmission dynamics on a global scale with a system of ordinary differen-tial equations describing dynamics on a local scale. This presentation highlights somerecent advancements in the Fortran software eBACOLI, an extension of BACOLI tothis multi-scale problem domain that brings along the error control features of theoriginal.

Meshfree finite difference methods for fully nonlinearelliptic equationsHamfeldt, Brittany (bdfroese@njit.edu)New Jersey Institute of Technology, Newark, USA

The relatively recent introduction of viscosity solutions and the Barles-Souganidisconvergence framework have allowed for considerable progress in the numerical so-lution of fully nonlinear elliptic equations. Convergent, wide-stencil finite differencemethods now exist for a variety of problems. However, these schemes are defined onlyon uniform Cartesian meshes over a rectangular domain. We describe a frameworkfor constructing convergent meshfree finite difference approximations for a class ofnonlinear elliptic operators. These approximations are defined on unstructured pointclouds, which allows for computation on non-uniform meshes and complicated ge-ometries. Because the schemes are monotone, they fit within the Barles-Souganidisconvergence framework and can serve as a foundation for higher-order filtered meth-ods. We present computational results for several examples including problems posedon random point clouds, problems with singular solutions, incorporation of automaticmesh adaptation, and problems in optimal transportation.

Parallel iterations for nonlinear boundary value prob-lemsHaynes, Ronald (rhaynes@mun.ca)Memorial University, St. John’s, Canada

In this talk we will consider iterations for relatively simple nonlinear boundaryvalue ordinary differential equations. We will review the construction of iterativeschemes which converge monotonically to solutions and require only a single linearsolve per iteration. We will then show how to parallelize the iterations.

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Function space MCMC for posteriors with non-GaussianpriorsHosseini, Bamdad (bamdadh@caltech.edu)California Institute of Technology, Pasadena, USA

We introduce a new class of Metropolis-Hastings algorithms for sampling targetmeasures that are absolutely continuous with respect to an underlying self-decomposableprior measure on infinite-dimensional Hilbert spaces. We particularly focus on mea-sures that are highly non-Gaussian and cannot be sampled effectively using conven-tional algorithms. We utilize the self-decomposability of the prior to construct anautoregressive proposal kernel that preserves the prior measure and satisfies detailedbalance.

Efficient Computation of Breaking Points in State-Dependent Delay Differential EquationsHumphries, Tony (tony.humphries@mcgill.ca)McGill University, Montreal, Canada

When state-dependent delay differential equation initial value problems are solvednumerically, the breaking points where the solution is not smooth must be com-puted concurrently with the solution. We show that breaking points where the solu-tion is only k-times differentiable with k < p must be approximated with accuracyO(hp/(k+1)), for step-size h, to retain the global order p of the method. We present anefficient algorithm for the detection and computation of breaking points in such prob-lems, without requiring an iterative procedure or step rejections to find the breakingpoint. This is achieved by solving a smooth modified problem at each step, where thesmooth problem has the same solution as the underlying problem until a breakingpoint is encountered. In this way both the location of and the solution up to thebreaking point are determined. Breaking points of any level k can be computed to upO(hp) accuracy, though for efficiency we usually only compute them for k < p. Thealgorithm is implemented with explicit Functional Continuous Runge-Kutta methodsand applied to test problems to demonstrate its efficacy.

An effective hybrid strategy for stochastic reaction-diffusion biochemical systems with delayIlie, Silvana (silvana@ryerson.ca)Ryerson University, Toronto, Canada

Many biochemical reactions, such as gene transcription and translation in a cell,require a certain time to finish once they are initiated. Stochastic simulation ofreaction-diffusion systems with delay can be computationally intensive. We proposea new hybrid algorithm to speed-up the stochastic simulation of delayed reaction-diffusion systems. The algorithm is designed for moderately stiff systems in which theevents may be partitioned into slow and fast subsets, depending on their propensities.The hybrid algorithm is tested on three benchmark problems and the results arecompared with those of the delayed Inhomogeneous Stochastic Simulation Algorithm.The numerical results show that the proposed hybrid algorithm is very efficient andhas very good accuracy.

This is joint work with A. Sayyidmousavi.

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Synthetic biology approaches to suppression of an-tibiotic resistance: toward model-based designIngalls, Brian (bingalls@uwaterloo.ca)University of Waterloo, Waterloo, Canada

Antibiotic-resistant pathogens present an increasing global health concern. Ourgroup is investigating synthetic biology-based strategies for suppression of resistancein environmental bacterial populations. This approach involves the delivery of en-gineered genetic elements to target populations. We are developing models of thedynamics of this system, at both the genetic and population level, to be used formodel-based design of potential implementations. Analysis of proof-of-principle sce-narios and accompanying experimental results will be presented.

Hybrizidable Discontinuous Galerkin Method for Lin-ear Free Surface ProblemsJones, Giselle Sosa (gsosajon@uwaterloo.ca)University of Waterloo, Waterloo, Canada

In this talk, we present the discretization of the free surface problem for irrotationalflows with linearized boundary conditions using the Local Hybridizable DiscontinuousGalerkin (L-HDG) method and the Interior Penalty Discontinuous Galerkin (IP-DG)method. The IP-DG case follows the work done by van der Vegt et al. in 2005.For the time discretization, we employ a BDF scheme. Through static condensation,the linear system to be solved on each time step in the HDG method is in generalsmaller than the one obtained with DG. Moreover, in L-HDG the gradient of thescalar variable converges with optimal rate, in contrast to IP-DG where the gradientconverges sub-optimally. L-HDG also allows superconvergence of the scalar variablethrough local postprocessing. We show two different numerical tests, one where theanalytical solution is known, and another one where we simulate waves generated bya wave maker. For the first case, we show the rates of convergence of both methodswhen using linear, quadratic and cubic polynomials.

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An Eulerian droplet model: Mathematical analysisand improvementKeita, Sana (skeit085@uottawa.ca)University of Ottawa, Ottawa, Canada

Air flows charged with particles occur in many biomedical, industrial and envi-ronmental applications. A common approach to simulate such flows is to solve theNavier-Stokes equations coupled with a second set of partial differential equationsrepresenting the volume fraction and average velocity of the particles at each pointin the domain. An hierarchy of these so-called Eulerian models of gas-particle flowshave been derived. When pressure forces are neglected or the same pressure is con-sidered for both phases, the resulting system is weakly hyperbolic and solutions mayexhibit vacuum states or delta shocks that are not physically desirable. Therefore,it is crucial to find a physical way for preventing the formation of such undesirablesolutions.

An Eulerian model was proposed for air-droplets flows. This model is successfullyused for the prediction of droplets impingement on airfoils and ice accretion on air-plane wings during in-flight icing. Extension to particle flows in airways was morerecently attempted. In our talk, we will show that the Eulerian model may developdelta shocks and vacuum states, and explain under which conditions delta shocksoccur. Next, a physical way for preventing the formation of delta shocks and vac-uum states in the model will be discussed and a new Eulerian droplet model will beproposed. Finally, 2D computations of air-particle flows comparing the new Euleriandroplet model with the standard droplet model will be presented.

Error Analysis of a Space-Time Hybridizable Discon-tinuous Galerkin Method for the Advection-DiffusionEquationKirk, Keegan (k4kirk@uwaterloo.ca)University of Waterloo, Waterloo, Canada

Many important applications of fluid mechanics require the solution of time-dependent partial differential equations on evolving and deforming domains. Notableexamples include the simulation of rotating wind turbines in strong air flow, waveimpact on offshore structures, and arterial blood flow in the human body.

A viable candidate for such problems is the space-time discontinuous Galerkin(DG) method. The problem is fully discretized in space and time instead of thetypical method of lines treatment of time-dependent problems on fixed domains. Theresulting scheme is well suited to handle moving and deforming domains, but at asignificant increase in computational cost in comparison to traditional time-steppingmethods. Attempts to rectify this situation have led to the pairing of space-timeDG with the hybridizable DG (HDG) method, which was developed solely to reducethe expense of DG. The combination of the two methods results in a scheme thatretains the high-order accuracy and geometric flexibility of space-time DG withoutthe associated computational burden.

We perform an a priori analysis of a space-time HDG method for the non-stationaryadvection-diffusion problem posed on a time-dependent domain. We discuss anisotropictrace and inverse inequalities valid for moving meshes, which are essential for our anal-ysis. Stability of the scheme is proven through the satisfaction of an inf-sup condition.Finally, we derive theoretical rates of convergence.

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A Fast Integral Equation Method for the Navier-Stokes Equations in 2DKlinteberg, Ludvig af (jafklint@sfu.ca)Simon Fraser University, Vancouver, Canada

Integral equation methods provide an efficient way of solving elliptic PDEs tohigh accuracy, particularly in complex geometries. They are however limited to ho-mogeneous problems, and have in the context of fluid dynamics mainly been used forsolving the Stokes equations. Recent years have seen development in the use of in-tegral equation methods also for inhomogeneous problems. In these hybrid methods,the solution is represented as a sum of a layer potential and a volume potential.

We will in this presentation discuss a high-order, hybrid integral equation methodfor the incompressible Navier-Stokes equations in 2D. The method is based on fastalgorithms for layer potentials and volume potentials, and is suitable for problemswith complex geometries and moderate Reynolds numbers.

Solving heat equation via a combined method of CPMand RBFLun, Chu Alex Shiu (alex chushiulun@yahoo.com.hk)University of British Columbia, Vancouver, Canada

The closest point method (CPM) is used to solve partial differential equations(PDEs) on surfaces. The method typically uses Lagrange interpolation and finite dif-ferences on a uniform grid surrounding the surface. In this work, we replace both theinterpolation and the finite differences with Radial Basis Function (RBF) techniques.This allows the method to work on scattered unstructured meshes and increases thesparsity of the linear algebra, especially in higher dimensions. This work study theaccuracy and efficiency of our approach on several PDEs and a variety of surfaces.

Preconditioned Iterative techniques for geophysicalelectromagnetic problemsMacLachlan, Scott (smaclachlan@mun.ca)Memorial University of Newfoundland, St. John’s, Canada

One of the ways to map the different conductive layers in Earth’s crust is toconstruct a so-called forward model in terms of Maxwell’s equations in the frequencydomain. A popular decomposition approach is to consider the vector potential andsolenoidal parts of the electrical field individually in the form of a coupled model.Suitable FEM discretization leads to a complex-valued block-structured matrix systemfor these two components; consequently, their equivalent real form is a 4x4 blockstructured system, half of which has a non-trivial nullspace due to the underlyingcurl-curl operator. In this talk, we present a block-structured preconditioner basedon the Auxiliary-space Maxwell Solver (AMS; Hiptmair-Xu) approach for the curl-curl blocks, augmented with appropriate treatment for the significant off-diagonalblocks in the coupled system.

This is joint work with Hisham bin Zubair Syed.

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Recent Advances in Gaussian Collocation Softwarefor Boundary Value ODEs and 1D PDEsMuir, Paul (muir@smu.ca)Saint Mary’s University, Halifax, Canada

We describe two numerical software projects that employ Gaussian collocation forthe error controlled numerical solution of boundary value ODEs (BVODEs) and 1Dtime-dependent PDEs, respectively.

Error control software returns an approximate solution for which an associatederror estimate satisfies a given user tolerance. This type of computation has twoimportant advantages: (i) the user can have reasonable confidence that the numericalsolution has an error that is consistent with the user tolerance, and (ii) the cost ofthe computation will typically be consistent with the requested accuracy.

The well-known error control Gaussian collocation BVODE solver, COLNEW,continues to be widely used; interfaces in Python, Scilab, and R have recently beendeveloped. Our BVODE project involves a major update of COLNEW; the newversion features a much simplified argument list, a superconvergent interpolant, anew error estimation scheme, and a new mesh refinement algorithm.

Our 1D PDE project features the new solver, BACOLRI, that is the most recentin the BACOL family of error control 1D PDE solvers. It implements new algorithmsfor interpolation-based spatial error estimation and spatial error control and is anupdate of the 1D PDE solver, BACOLR, which implements Gaussian collocation forthe spatial discretization coupled with a Runge-Kutta solver for the time integration.We have also developed a Python interface for BACOLRI.

A class of 2D coupled bulk-surface reaction-diffusionmodels and their bifurcation analysisPaquin-Lefebvre, Frederic (paquinl@math.ubc.ca)University of British Columbia, Vancouver, Canada

In this talk, a class of coupled bulk-surface reaction-diffusion systems is considered.Passive diffusion occurs on both the bulk domain and its boundary, whereas nonlinearreaction kinetics are restricted to the later one. For the circular bulk case, we presenthow to systematically derive normal forms near the onset of oscillatory and symmetry-breaking instabilities. The theory is illustrated using classical Schnakenberg andBrusselator reaction kinetics, and good agreement between numerical and analyticalsolutions is obtained in the weakly nonlinear regime. Since our analysis is motivatedby applications in cell biology, the extension of it to the study of spatio-temporalprotein oscillations will be broached.

This is a joint work with Michael Ward and Wayne Nagata, UBC.

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Cell Polarization and Growth in Yeast MatingPetzold, Linda (petzold@cs.ucsb.edu)University of California Santa Barbara, Santa Barbara, USA

Polarization is an essential behavior of living cells, yet the dynamics of thissymmetry-breaking process are not fully understood. We have developed a spatialstochastic model of cellular polarization during mating of Saccharomyces cerevisiae.Specifically we investigated the ability of yeast cells to sense a spatial gradient of mat-ing pheromone and respond by forming a projection in the direction of the matingpartner. Our results demonstrated that a spatial stochastic model of polarisome for-mation can more robustly reproduce two fundamental characteristics observed in wild-type cells: a tightly polarized phenotype and the ability to track moving pheromoneinput, in comparison with the corresponding deterministic model.

Existing models of cell polarization have focused solely on the biochemical sig-naling system. However, there exists a well-known interplay between the growth ofthe mating projection and the mechanical forces of the cell wall in determining theshape of the cell. The cell wall of S. cerevisiae both defines its shape and provides themechanical integrity necessary to sustain the large internal turgor pressure. Underthe isotropic push of turgor pressure, polarized expansion occurs via localized assem-bly of new cell wall material in combination with a simultaneous softening of the cellwall, inducing it to yield and locally expand. Intracellular signaling directs enzymeswith the ability to modify cross-linking of polymers in the cell wall to the region ofpolarization. The resulting mechanical feedback from the wall expansion initiates thedelivery of raw material via vesicular transport.

To accurately model this complex biological phenomena, we have developed amultiscale computational framework for simulating the coupling of the stochasticdynamics of biochemical reactions involved in shaping walled cells to the mechanicalprocesses of cell wall expansion and growth. Our computational method exploits thetime-scale separation between the relatively slow dynamics of the cell wall and therapid interactions of the intercellular signaling network.

Weakly compressible flow through a cylinder withdensity-dependent viscosity and Navier-slip at thewallRohlf, Katrin (krohlf@ryerson.ca)Ryerson University, Toronto, Canada

Flow of an incompressible fluid with density-dependent viscosity and Navier-slipat the wall is considered for flow through a cylinder. A perturbation solution withcompressibility as a perturbation parameter is derived, and compared to a finite-element solution. It is shown that the second-order perturbation solution agrees wellwith the finite-element solution for the parameter values considered. Changes inflow for different Reynolds numbers, Froude numbers, aspect ratios, compressibilities,density-dependent viscosity parameters and slip values will be presented.

This was joint work with L. Regmi and A. Sayyidmousavi.

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Arbitrary order A-stable methods for Ordinary dif-ferential Equations via deffered correctionSaint-Cyr, Koyaguerebo-Ime (skoya005@uottawa.ca)University of Ottawa, Ottawa, Canada

It is well known that “the order of an A-stable linear multistep method can not ex-ceed 2. The smallest error constant, c∗ = 1/12, is obtain for the trapezoidal rule,..”1.In our talk, we will show that via a convenient deffered correction method this severerestriction can be easily overcame. We present a sequence of self-starting defferedcorrection (DC) schemes built recursively from a modified trapezoidal rule (Crank-Nicholson) for the numerical solution of ordinary differential equations (ODE). Weprove that each scheme is A-stable and that the correction on a scheme DC2j (oforder 2j of accuracy) leads to a scheme DC(2j+2) (of order 2j+2). Our proof is basedon a deffered correction condition (DCC) which guarantees the order of accuracy. Wewill also explain how other schemes (e.g. from the BDF or RK families) satisfyingthe DCC can be corrected to increase the order of accuracy successively by two. Nu-merical experiments from standard stiff ODEs are performed with the DC2, ..., DC10schemes. We will show that the expected orders of accuracy are achieved togetherwith excellent stability of the method. Co-author: Yves Bourgault.

Multi-Particle Collision Dynamics for Modeling Reaction-Diffusion SystemsSayyidmousavi, Alireza (asayyidmousavi@ryerson.ca)Ryerson University, Toronto, Canada

Two important issues on using Reactive Multi-Particle Collision (RMPC) Dynam-ics for modelling reaction-diffusion systems are discussed. First, maintaining the apriori diffusion coefficient of the particles throughout the simulation. Second, mod-elling partially adsorbing boundary conditions. To tackle the first issue, the use of theso-called bath particles, whose purpose is only to ensure proper diffusion of the mainparticles in the system, is suggested. The second issue is dealt with by establishing ananalogy between the RMPC and Brownian Dynamics. Sample results and discussionsare also presented.

1Citation from [Wanner, Dahlquist’s classical papers on stability theory, BIT, 2006].

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Microscopic Models of Synthetic NanomotorsSchofield, Jeremy (jmschofi@chem.utoronto.ca)University of Toronto, Toronto, Canada

Active systems of synthetic motors operating out of equilibrium on nanoscaleshave unique properties that can be exploited in applications in a number of differentfields, and the descriptions of the mechanisms by which they operate present chal-lenges for theory and simulation. In this talk synthetic chemically-propelled Janusmotors without moving parts that operate by a diffusiophoretic mechanism will bediscussed, where self-generated concentration gradients are responsible for motor mo-tion. Janus motors with chemically active and inactive hemispheres can operate onlyunder nonequilibrium conditions where detailed balance is broken by fluxes of chemi-cal species that establish a nonequilibrium state. A microscopic model is constructedto study Janus particle reactive dynamics. The system is driven into a nonequilibriumsteady state by fluxes of chemical species that control the chemical affinity. While dif-ferent motor geometries are discussed, Janus motors with catalytic and noncatalyticportions are used to illustrate the unusual nonequilibrium behavior of active systems,including giant number fluctuations, dynamic phase separation, directed motion andenhanced diffusion. Single motor motion, the collective dynamics of many motors,and the dynamics of motors in crowed media will be discussed.

Elliptic PDEs on composite domains via the Schwarzalternating method and the Closest Point MethodShao, Aili (ali.shao@math.ubc.ca)University of British Columbia, Vancouver, Canada

The Schwarz alternating method is an iterative domain decomposition methodfor solving elliptic problems on a domain consisting of overlapping subdomains. Inthis talk, we study an algorithm combining the Schwarz alternating method with theClosest Point Method to solve elliptic boundary value problems on general compositedomains. The algorithm embeds each subdomain into a larger regular domain, whereCartesian finite differences can be easily applied. We deal with the resulting mixed-boundary conditions using a ghost point approach. Convergence results are comparedwith a finite element approach.

A spectral method for nonlocal diffusion operatorson the sphereSlevinsky, Richard Mikael (richard.slevinsky@umanitoba.ca)University of Manitoba, Winnipeg, Canada

We present algorithms for solving spatially nonlocal diffusion models on the unitsphere with spectral accuracy in space. Our algorithms are based on the diagonaliz-ability of nonlocal diffusion operators in the basis of spherical harmonics, the compu-tation of their eigenvalues to high relative accuracy using quadrature and asymptoticformulas, and a fast spherical harmonic transform. These techniques also lead toan efficient implementation of high-order exponential integrators for time-dependentmodels. We apply our method to the nonlocal Poisson, Allen–Cahn and Brusselatorequations.

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High-Order Operator-Splitting Methods for the Bido-main and Monodomain ModelsSpiteri, Raymond (spiteri@cs.usask.ca)University of Saskatchewan, Saskatoon, Canada

The bidomain and monodomain models are among the most widely used mathe-matical models to describe cardiac electrophysiology. They take the form of multi-scale reaction-diffusion partial differential equations that couple the dynamic be-haviour on the cellular scale with that on the tissue scale. The systems of differentialequations associated with these models are large and strongly non-linear, but they alsohave a distinct structure due to their multi-scale nature. For these reasons, numericalsolutions to these systems are often found via operator-splitting methods. The focusof this presentation is on operator-splitting methods with order higher than two that,according to the Sheng–Suzuki theorem, require backward time integration and his-torically have been considered unstable for solving deterministic parabolic systems.The stability and performance of operator-splitting methods of up to order four tosolve the bidomain and monodomain models are demonstrated on several examplesarising in the field of cardiovascular modeling.

Controlling diffusion in Reactive Multiparticle Colli-sion DynamicsStrehl, Robert (robertstrehl@web.de)Industry, , Germany

Microscopic simulation methods that are based on Brownian Dynamics typicallyhave a computational complexity of O(N2). A less complex alternative is ReactiveMultiparticle Collision Dynamics (RMPC). In this talk I present an extension toRMPC where species-dependent diffusion coefficients are considered. Particular chal-lenges that arise in the presence of low average numbers of particles in computationalvoxels are discussed. To promote the validity the framework is applied on a signalingpathway for bacterial chemotaxis.

This is a presentation of joint work with Katrin Rohlf carried out at RyersonUniversity.

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Resilience of network synchronization against struc-tural and dynamical perturbationsSun, Jie (sunj@clarkson.edu)Clarkson University, New York, USA

Synchronization of network coupled systems is an important research topic, es-pecially given its broad engineering and biological applications, for example in brainwaves, power grids, and animal behavior. In practice, a system almost never operatesin the absence of changes or perturbations, and consequently, a central question ishow these perturbations might affect synchronization. Existing work through the useof master stability analysis focuses either on a networks synchronizability (resilienceagainst change of coupling strength) or linear stability of synchronization (resilienceagainst infinitesimal dynamical perturbations). In this work, we focus on generalstructural and dynamical perturbations, providing analytical tools to measure theireffects on network synchronization, and show (through numerical simulations) thatinteresting nonlinear correlation seems to exist between a networks structural anddynamical resilience. To illustrate the importance of our analysis, we show examplesof where cospectral networks, whose synchronization properties are identical undermaster stability analysis, nevertheless exhibits drastically synchronization dynamics:some synchronize slower than the others, and some do not synchronize at all (despitebeing predicted otherwise using corresponding linearized dynamics).

Fitting a Stochastic Model to Eye Movement TimeSeriesTupper, Paul (pft3@sfu.ca)Simon Fraser University, Vancouver, Canada

Our goal is to develop an efficient framework for fitting stochastic continuous-timemodels to experimental data in cognitive psychology. As a simple test problem, weconsider data from an eye-tracking study of attention in learning. For each subject, thedata for each trial consists of the sequence of stimulus features that the subject fixateson, together with the duration of each fixation. We fit a stochastic differential equationmodel to this data, using the Approximate Bayesian Computation framework. Foran individual subject we infer posterior distributions for the unknown parameters inthe model.

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Numerical Method for Solving Optimal Mass Trans-port arising from Image RegistrationWan, Justin (jwlwan@uwaterloo.ca)University of Waterloo, Waterloo, Canada

We propose fast, accurate and convergent numerical methods for solving optimalmass transport problem arising from image registration. In addition, we proposeto use periodic boundary condition instead of Neumann boundary condition so thatwe are able to recover translation in the non-rigid deformation. To solve the modelequation, we first transform the nonlinear PDEs into an HJB equation. We apply amixed standard 7-point stencil and semi-Lagrangian wide stencil discretization, suchthat the numerical solution is guaranteed to converge to the viscosity solution ofthe Monge-Ampere equation. We design a numerical scheme that converges to theoptimal transformation between the target and template images. Finally, we developfast multigrid methods for solving the discrete nonlinear system. In particular, wepropose a four-directional alternating line relaxation scheme as smoother, and a newcoarsening strategy where wide stencil points are set as coarse grid points. Ournumerical results show that the numerical solution yield good quality transformationsfor non-rigid image registration and the convergence rates of the proposed multigridmethods are mesh-independent.

A numerical method for solving ODEs on surfacesWong, Tony (kawahtony@gmail.com)University of British Columbia, Vancouver, Canada

Modelling particle dynamics is fundamental in studying dynamical systems. How-ever, generalization of well-developed ODE solvers for handling dynamics on generalsurfaces is lacking, due to the complication from the surface metric. In this talk, weintroduce a simple yet efficient numerical algorithm for solving ODEs on arbitrarysurfaces, based on local reconstruction.

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An Hermite-Obreschkoff Method for Stiff High-IndexDAEsZolfaghari, Reza (zolfaghr@mcmaster.ca)McMaster University, Hamilton, Canada

We are interested in solving high-index differential-algebraic equations (DAEs).The DAETS solver by Nedialkov and Pryce can integrate numerically high-index,arbitrary order DAE systems. Based on explicit Taylor series, this solver is efficienton non-stiff to mildly stiff problems, but due to stability restrictions, it takes verysmall steps on highly stiff problems.

Hermite-Obreschkoff (HO) methods can be viewed as a generalization of Taylorseries methods. The former have smaller truncation error than the latter, and haveexcellent stability properties: an implicit HO method can be A- or L- stable. ImplicitHO methods are challenging to implement due to the required higher-order derivativesand Jacobians.

We develop such a method for numerical solution of stiff high-index DAEs. As inDAETS, our method employs Pryce’s structural analysis to determine the constraintsof the problem and to organize the computations of higher-order derivatives for thesolution, which are obtained through automatic differentiation. We discuss the overallintegration scheme: finding a consistent initial point, computing an initial guess forNewton’s method, automatic differentiation for constructing the needed Jacobians init, and stepsize control. We report numerical results on several stiff DAE and ODEsystems illustrating the performance of this method, and in particular its ability totake large steps on stiff problems.

Joint work with N. Nedialkov, McMaster University.

21

List of speakers

1. Bihlo, Alex (abihlo@mun.ca)Memorial University of Newfoundland, St. John’s, Canada

2. Cao, Young (Yang) (ycao@cs.vt.edu)Virginia Tech, Blacksburg, USA

3. Cervi, Jessica (jessica.cervi@usask.ca)University of Saskatchewan, Saskatoon, Canada

4. Chan, Eunice (echan295@uwo.ca)University of Western Ontario, London, Canada

5. Dominguez, Sebastian (domingue@sfu.ca)Simon Fraser University, Vancouver, Canada

6. Do Pham, Martin (martindopham@gmail.com)University of Waterloo, Waterloo, Canada

7. Faeder, James (faeder@pitt.edu)University of Pittsburgh, Pittsburgh, USA

8. Fokoue, Diane (dfoko042@uottawa.ca)University of Ottawa, Ottawa, Canada

9. Gholami, Samaneh (samaneh.gholami@ryerson.ca)Ryerson University, Toronto, Canada

10. Green, Kevin (kevin.green@usask.ca)University of Saskatchewan, Saskatoon, Canada

11. Hamfeldt, Brittany (bdfroese@njit.edu)New Jersey Institute of Technology, Newark, USA

12. Haynes, Ronald (rhaynes@mun.ca)Memorial University, St. John’s, Canada

13. Hosseini, Bamdad (bamdadh@caltech.edu)California Institute of Technology, Pasadena, USA

14. Humphries, Tony (tony.humphries@mcgill.ca)McGill University, Montreal, Canada

15. Ilie, Silvana (silvana@ryerson.ca)Ryerson University, Toronto, Canada

16. Ingalls, Brian (bingalls@uwaterloo.ca)University of Waterloo, Waterloo, Canada

17. Jones, Giselle Sosa (gsosajon@uwaterloo.ca)University of Waterloo, Waterloo, Canada

18. Keita, Sana (skeit085@uottawa.ca)University of Ottawa, Ottawa, Canada

19. Kirk, Keegan (k4kirk@uwaterloo.ca)University of Waterloo, Waterloo, Canada

20. Klinteberg, Ludvig af (jafklint@sfu.ca)Simon Fraser University, Vancouver, Canada

21. Lun, Chu Alex Shiu (alex chushiulun@yahoo.com.hk)University of British Columbia, Vancouver, Canada

22

22. MacLachlan, Scott (smaclachlan@mun.ca)Memorial University of Newfoundland, St. John’s, Canada

23. Muir, Paul (muir@smu.ca)Saint Mary’s University, Halifax, Canada

24. Paquin-Lefebvre, Frederic (paquinl@math.ubc.ca)University of British Columbia, Vancouver, Canada

25. Petzold, Linda (petzold@cs.ucsb.edu)University of California Santa Barbara, Santa Barbara, USA

26. Rohlf, Katrin (krohlf@ryerson.ca)Ryerson University, Toronto, Canada

27. Saint-Cyr, Koyaguerebo-Ime (skoya005@uottawa.ca)University of Ottawa, Ottawa, Canada

28. Sayyidmousavi, Alireza (asayyidmousavi@ryerson.ca)Ryerson University, Toronto, Canada

29. Schofield, Jeremy (jmschofi@chem.utoronto.ca)University of Toronto, Toronto, Canada

30. Shao, Aili (ali.shao@math.ubc.ca)University of British Columbia, Vancouver, Canada

31. Slevinsky, Richard Mikael (richard.slevinsky@umanitoba.ca)University of Manitoba, Winnipeg, Canada

32. Spiteri, Raymond (spiteri@cs.usask.ca)University of Saskatchewan, Saskatoon, Canada

33. Strehl, Robert (robertstrehl@web.de)Industry, , Germany

34. Sun, Jie (sunj@clarkson.edu)Clarkson University, New York, USA

35. Tupper, Paul (pft3@sfu.ca)Simon Fraser University, Vancouver, Canada

36. Wan, Justin (jwlwan@uwaterloo.ca)University of Waterloo, Waterloo, Canada

37. Wong, Tony (kawahtony@gmail.com)University of British Columbia, Vancouver, Canada

38. Zolfaghari, Reza (zolfaghr@mcmaster.ca)McMaster University, Hamilton, Canada

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Daily Schedule

Monday, June 4, 2018

Computational Mathematics and Applications, 10h15-12h15, Drama Room 4

10h15: Cao, Young (Yang), Accuracy Analysis of Hybrid Stochastic Simulation Algo-rithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p.510h45: Schofield, Jeremy, Microscopic Models of Synthetic Nanomotors . . . . . . . . . . . p.1711h15: Strehl, Robert, Controlling diffusion in Reactive Multiparticle Collision Dynamicsp.1811h45: Fokoue, Diane, Numerical methods for the microscopic cardiac electrophysiologymodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.8

Scientific Computing - Contributed Talks, 10h15-12h15, Drama Room 7

10h15: Sun, Jie, Resilience of network synchronization against structural and dynamicalperturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.1910h45: Saint-Cyr, Koyaguerebo-Ime, Arbitrary order A-stable methods for Ordinarydifferential Equations via deffered correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.1611h15: Muir, Paul, Recent Advances in Gaussian Collocation Software for BoundaryValue ODEs and 1D PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.1411h45: Humphries, Tony, Efficient Computation of Breaking Points in State-DependentDelay Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.10

Computational Mathematics and Applications, 16h00-18h00, Drama Room 4

16h00: Faeder, James, Rule-based modeling of biochemical systems. . . . . . . . . . . . . . . . . .p.716h30: Ingalls, Brian, Synthetic biology approaches to suppression of antibiotic resistance:toward model-based design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.1017h00: Ilie, Silvana, An effective hybrid strategy for stochastic reaction-diffusion bio-chemical systems with delay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p.1017h30: Spiteri, Raymond, High-Order Operator-Splitting Methods for the Bidomain andMonodomain Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.18

Scientific Computing - Contributed Talks, 16h00-17h30, Rehearsal Hall 1

16h00: Haynes, Ronald, Parallel iterations for nonlinear boundary value problems . . p.916h30: Slevinsky, Richard Mikael, A spectral method for nonlocal diffusion operatorson the sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p.1717h00: Lun, Chu Alex Shiu, Solving heat equation via a combined method of CPM andRBF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.13

Tuesday, June 5, 2018

Minisymposium on Scientific Computing, 10h00-12h00, Drama Room 4

10h00: Bihlo, Alex, A well-balanced meshless tsunami propagation and inundation modelp.510h30: Hamfeldt, Brittany, Meshfree finite difference methods for fully nonlinear ellipticequations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.911h00: Cervi, Jessica, Towards new high-order operator-splitting time-integrationmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p.611h30: Dominguez, Sebastian, An overdetermined eigenvalue problem in linear elasticityp.6

Plenary Talk, 14h00-15h00, Rehearsal Hall 2

14h00: Petzold, Linda, Cell Polarization and Growth in Yeast Mating . . . . . . . . . . . . . . p.15

Wednesday, June 6, 2018

Computational Mathematics and Applications, 10h00-12h00, Drama Room 4

10h00: Sayyidmousavi, Alireza, Multi-Particle Collision Dynamics for ModelingReaction-Diffusion Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.1610h30: Paquin-Lefebvre, Frederic, A class of 2D coupled bulk-surface reaction-diffusionmodels and their bifurcation analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.1411h00: Gholami, Samaneh, Model reduction of Stochastic Models of BiochemicalSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.811h30: MacLachlan, Scott, Preconditioned Iterative techniques for geophysical electro-magnetic problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.13

Wednesday, June 6, 2018 (cont’d)

Scientific Computing - Contributed Talks, 10h00-12h00, Drama Room 7

10h00: Green, Kevin, Extended BACOLI: Solving one-dimensional multi-scale parabolicPDE systems with error control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.910h30: Kirk, Keegan, Error Analysis of a Space-Time Hybridizable DiscontinuousGalerkin Method for the Advection-Diffusion Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.1211h00: Shao, Aili, Elliptic PDEs on composite domains via the Schwarz alternatingmethod and the Closest Point Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p.17

Minisymposium on Scientific Computing, 15h30-17h30, Drama Room 4

15h30: Rohlf, Katrin, Weakly compressible flow through a cylinder with density-dependent viscosity and Navier-slip at the wall. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p.1516h00: Tupper, Paul, Fitting a Stochastic Model to Eye Movement Time Series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p.1916h30: Wong, Tony, A numerical method for solving ODEs on surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p.2017h00: Hosseini, Bamdad, Function space MCMC for posteriors with non-Gaussianpriors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.10

Scientific Computing - Contributed Talks, 15h30-17h00, Rehearsal Hall 1

15h30: Jones, Giselle Sosa, Hybrizidable Discontinuous Galerkin Method for Linear FreeSurface Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p.1116h00: Klinteberg, Ludvig af, A Fast Integral Equation Method for the Navier-StokesEquations in 2D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p.1216h30: Keita, Sana, An Eulerian droplet model: Mathematical analysis and improvement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .p.12

Thursday, June 7, 2018

Scientific Computing, Contributed Talks, 9h00-11h00, Drama Room 4

9h00: Wan, Justin, Numerical Method for Solving Optimal Mass Transport arising fromImage Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.209h30: Zolfaghari, Reza, An Hermite-Obreschkoff Method for Stiff High-Index DAEs p.2010h00: Chan, Eunice, Algebraic Linearizations of Matrix Polynomials. . . . . . . . . . . . . . . .p.610h30: Do Pham, Martin, Visualizing fractal patterns in DNA sequences using chaosgame representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . p.7