fisika komputasi (computational...
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FISIKA KOMPUTASI
(COMPUTATIONAL PHYSICS)
IshafitProgram Studi Pendidikan Fisika – Universitas Ahmad Dahlan
What is Computational Physics
Reference: Resource Letter CP-2: Computational Physics
Rubin H. Landau, Am. J. Phys. 76 4&5, April/May 2008
What is Computational Physics ?
1. Process and analyze large amounts of data from measurements; fit
to theoretical models; display and animate graphically
Ex: search for "events" in particle physics, image analysis in
astronomy.
2. Numerical solution of equations that cannot be accomplished by
analytical techniques (coupled, nonlinear etc.)
Ex: fluid dynamics (Navier Stokes), numerical relativity (Einstein's
field equations), electronic ground state wavefunctions in solid state
systems, nonlinear growth equations
3. Computer "experiments": simulate physical phenomena, observe
and extract quantities as in experiments, explore simplified model
systems for which no solution is known.
Ex: molecular simulations of materials, protein folding, planetary
dynamics (N-body dynamics).
What is Computational Physics?
Computational Physics combines physics, computer science
and applied mathematics in order to provide scientific
solutions to realistic and often complex problems.
Areas of application include the nature of elementary
particles, the study and design of materials, the study of
complex structures (like proteins) in biological physics,
environmental modeling, and medical imaging.
A computational physicist understands not only the
workings of computers and the relevant science and
mathematics, but also how computer algorithms and
simulations connect the two.
Theory - Computation - Experiment
Theoretical Physics
Construction and mathematical
(analytical) analysis of idealized
models and hypotheses to
describe nature
Experimental Physics
Quantitative measurement
of physical phenomena
Computational PhysicsPerforms idealized "experiments"
on the computer, solves physical
models numerically
predicts
tests
Computation across all areas of physics
High Energy Physics: lattice chromodynamics, theory of the strong interaction, data analysis from accelerator experiments
Astronomy and Cosmology: formation and evolution of solar systems, star systems and galaxies
Condensed Matter Physics:- electronic structure of solids and quantum effects- nonlinear and far from equilibrium processes - properties and dynamics of soft materials such as polymers,
liquid crystals, colloids
Biophysics: simulations of structure and function of biomolecules such as proteins and DNA
Materials Physics: behavior of complex materials, metals, alloys, composites
Career Opportunities for Computational Physicists
• A graduate degree in physics in areas such as biophysics,
condensed matter physics, particle physics, astrophysics to name a
few.
• A career in High-performance and scientific computing, in the
energy and aerospace sectors, with chemical and pharmaceutical
companies, with environmental management agencies.
• Employment in firms that develop scientific software, as well as
computer games.
• A research career in an academic, industrial, or national laboratory
• A teaching career in physics
• A job in Wall Street. Even Wall Street employers are interested in
people with a background in computational physics.
Journals and Magazines…
Syllabus
Modelling and Error Analysis
Mathematical Modeling A Simple Mathematical Model
Approximations and Round-Off Errors Significant Figures Accuracy and Precision Error Definitions Round-Off Errors
Truncation Errors and the Taylor Series The Taylor Series Error Propagation Total Numerical Error
Syllabus
Taking derivatives
General discussion of derivatives with computers
Forward difference
Central difference and higher order methods
Higher order derivatives
Solution of nonlinear equations
Bisection method
Newton’s method
Method of secants
Brute force method
Syllabus
Interpolation
Lagrange interpolation
Neville’s algorithm
Linear interpolation
Polynomial interpolation
Cubic spline
Numerical integration
Introduction to numerical integration
The simplest integration methods
More advanced integration
Syllabus
Matrices
Linear systems of equations
Gaussian elimination
Standard libraries
Eigenvalue problem
Differential equations
Introduction
A brush up on differential equations
Introduction to the simple and modified Euler methods
The simple Euler method
The modified Euler method
Runge–Kutta method
Adaptive step size Runge–Kutta
The damped oscillator
Fundamental Convictions
In approaching problems in physics, physicists
• Solve algebraic equations
• Solve ordinary differential equations
• Solve partial differential equations
• Evaluate integrals
• Find roots, eigenvalues, and eigenvectors
• Acquire and analyze data
• Graph functions and data
• Fit curves to data
• Manipulate Images
• Prepare reports and papers