hardware acceleration of computional fluid dynamics simulations in an oxygenator - part 1

Politecnico di MilanoDipartimento di Elettronica, Informazione e Bioingegneria (DEIB)

Hardware Acceleration of

Computational Fluid Dynamics

Simulations in an Oxygenator

Introduction and State of the Art

Chiara [email protected]

B3Lab, May 4th 2016

Guido [email protected]

HAMSproject

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The context

Wojchiec Zasina and Philip Hogeboom (from the Noun Project)

Cardiac Surgery

When we need to operate

the patient’s hearth,

but

we can’t stop the

circulation for too long...

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Extra-Corporeal Circulation

(ECC)

www.medici-italia.com

The context

1) Venous blood picked up from the

caval veins

2) Blood treatment (heating,

oxygenation, ...)

3) Treated blood re-inserted into

arterial system

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www.medici-italia.com

The context

OXYGENATOR

Extra-Corporeal Circulation

(ECC)

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Oxygenator

www.lookfordiagnosis.com

● THE FUNCTION

Replicate the lungs’ task:

- pick up CO2 from blood

- put O2 into blood

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Oxygenator

www.perfusione.net

● THE FUNCTION

Replicate the lungs’ task:

- pick up CO2 from blood

- put O2 into blood

● HOW IT IS MADE

Many different

membranes rolled up

concentrically

→ porous system

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Oxygenator

www.perfusione.net

In order to optimize

the design

Need to know blood

behaviour

CFD simulations

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Fluid dynamics can be studied through:

Oxygenator

FEM

(Finite Element

Method)

Lumped

parameters

model

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Oxygenator

FEM

(Finite Element

Method)


fast and accurate

but

complex and expensive

Lumped

parameters

model

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Oxygenator

FEM

(Finite Element

Method)


fast and accurate

but


Lumped

parameters

model

easy and low-cost

but

trade-off time vs accuracy

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Oxygenator

FEM

(Finite Element

Method)


fast and accurate

but


Lumped

parameters

model

the linear system generated by

the model is solved through

matrix inversion

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Oxygenator

FEM

(Finite Element

Method)


fast and accurate

but


Lumped

parameters

model

implementation in MATLAB(versatile, easy-to-use, widespread)

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The problem

https://thenounproject.com/

If only MATLAB simulations

could take less time...

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The idea

https://thenounproject.com/

If only MATLAB simulations

could take less time...

HARDWARE

ACCELERATION

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The device

FPGAs Speedup wrt common

processors

Low power requirements

Programmability

Affordable costs

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Our goal

Study an oxygenator for ECC through a lumped

parameters model in MATLAB and accelerate the

simulation by means of an FPGA-based system

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Our goal




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Our goal




Lumped

parameters

model

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Our goal




Lumped

parameters

model

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Our goal




Lumped

parameters

model

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State of the

Art

Matlab HDL Coder HW matrix inversion

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State of the

Art

- Matrices can not be

passed directly as I/O (but

can be managed internally)

- Requires HW-adapted

algorithms (eg. CORDIC)


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State of the

Art

- Matrices can not be

passed directly as I/O (but

can be managed internally)

- Requires HW-adapted

algorithms (eg. CORDIC)

NOT TRIVIAL


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State of the

Art

AlgorithmsApplicative

domains


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Applicative domains

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Algorithms

SVD method°Greville’s algorithmFull rank QR

factorization

Moore-Penrose Pseudo Inverse*

* Corrieu P, «Fast Computation of Moore-Penrose Inverse Matrices», Neural Information Processing, 2005

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factorization


Let be A = U*∑*V’ then pinv(A) = V*pinv(∑)*U’

Very accurate method

But

Time consuming for large matrices

(because of SVD)

* Corrieu P, «Fast Computation of Moore-Penrose Inverse Matrices», Neural Information Processing, 2005

Algorithms

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factorization

° Rahmati et al, “FPGA Based Singular Value Decomposition for Image Processing Applications ”, 2008

QR algorithm

Computationally efficient

Hemkumar, "A systolic VLSI architecture

for complex SVD", 1992

Jacobi method

More accurate, parallelism

Luk, Park, "A proof of convergence for two

parallel Jacobi SVD algorithms", 2002


Algorithms

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Singular Value Matlab* FPGA % error

σ1 2.6603 2.7500 3.3718

σ2 2.3113 2.3125 0.0519

Elapsed Time 2.7141 s 24.3143 ms

SVD Computation of a 32x127 Matrix: this table shows the corresponding

singular values with the minimum and maximum estimation errors for the

case of a 32 x 127 matrix. This table also shows the elapsed time for the

software and hardware implementations.*Matlab 7.3.0.267 utilizing 2.4GHz Intel Core Duo Processor

“Reconfigurable FPGA-Based Unit for Singular Value Decomposition

of Large m x n Matrices”, Ledesma-Carrillo et al., 2011

Some results

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Matlab HDL coder HW matrix inversion

Our contributionvs vs

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Our contributionvs

Managing of the whole

interface

It is not needed to write

HDL-friendly Matlab code

(only function)

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Our contributionvs

Management of larger matrices

(up to 8000x8000)

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Our contributionvs

Management of larger matrices

(up to 8000x8000)

through

i) strong parallelism

ii) streaming in data transfer

iii) Xilinx Virtex 7 VC707

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QUESTIONS?

Contact us!

HAMSproject

[email protected]

[email protected]

[email protected]

www.facebook.com/hams.project

https://twitter.com/HAMS_project

http://www.slideshare.net/HAMSproject

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References[1] Wang et al, “A CORDIC-Based Dynamically Reconfigurable FPGA Architecture for Signal Processing Algorithms”, 2008

[2] Burian et al, “A Fixed-Point Implementation of Matrix Inversion Using Cholesky Decomposition”, 2004

[3] Bigdeli et al, “A New Pipelined Systolic Array-Based Architecture for Matri Inversion in FPGAs with Kalman Filter Case Study”, 2005

[4] Edmann et al, “A Scalable Pipelined Complex Valued Matrix Inversion Architecture”, 2005

[5] Garcia et al, “A Suitable FPGA Implementation of Floating-Point Matrix Inversion Based on Gauss-Jordan Elimination», 2011

[6] Ahmedsaid et al, “Accelerating SVD on Reconfigurable Hardware for Image Denoising”, 2004

[7] Kumar et al, “An Approach to Design a Matrix Inversion HW Module using FPGA”, 2014

[8] Irturk et al, “An Efficient FPGA Implementation of Scalable Matrix Inversion Core usign QR Decomposition”, 2009

[9] Norton et al, “An Evaluation of the Xilinx Virtex-4 FPGA for On-Board Processin in an Advanced Imaging System”, 2009

[10] Irturk et al, “An FPGA Design Space Exploration Tool for Matrix Inversion Archiectures”, 2008

[11] Ma et al, “An FPGA-based Singular Value Decomposition Processor ”, 2006

[12] Wu et al, “Approximate Matrix Inversion for High-Throughput Data Detection in the Large-Scale MIMO Uplink ”, 2013

[13] Irturk et al, “Automatic Generation of Decomposition based Matrix Inversion Architectures ”, 2008

[14] Szekowka et al, “CORDIC and SVD Implementation in Digital Hardware ”, 2010

[15] Sergiyenko et al, “Error-Free Computation of Inverse Matrices in FPGA ”, 2013

[16] Rahmati et al, “FPGA Based Singular Value Decomposition for Image Processing Applications ”, 2008

[17] Grammenos et al, “FPGA Design of a Truncated SVD Based Receiver for the detection of SEFDM Signals ”, 2011

[18] Karkooti et al, “FPGA Implementation of Matrix Inversion Using QRD-RLS Algorithm”, 2005

[19] Blace et al, “High level Prototyping and FPGA Implementation of the Orthogonal Matching Pursuit Algorithm ”, 2012

[20] Ahmedsaid et al, “Improved SVD Systolic Array and Implementation on FPGA”, 2003

[21] S. Hu and Q. Yan, “Inversion of Vandermonde Matrices in FPGAs ”, 2004

[22] Ohta et al, “Matrix Decomposition Suitable for FPGA Implementation of N-continuous OFDM ”, 2014

[23] Chisty et al, “Matrix Inversion Using QR Decomposition by Parabolic Synthesis ”, 2012

[24] Ma et al, “QR Decomposition-Based Matrix Inversion for High Embedded MIMO Receivers ”, 2011

[25] Wernke et al, “Real-Time Data Processing for an Advanced Imaging System Using the Xilinx Virtex-5 FPGA ”, 2009

[26] Ledesma-Carrillo et al, “Reconfigurable FPGA-Based Unit for Singular Value Decomposition of Large mxn Matrices ”, 2011

[27] Wang et al, “Singular Value Decomposition Hardware for MIMO - State of the Art and Custom Design ”, 2010

hardware acceleration of computional fluid dynamics simulations in an oxygenator - part 1

Devices & Hardware