FISIKA KOMPUTASI

(COMPUTATIONAL PHYSICS)

IshafitProgram Studi Pendidikan Fisika – Universitas Ahmad Dahlan

What is Computational Science

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.

Computational Physics

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

3 Pillars

TheoryComputational

Physics Experiment

4 Pillars?

TheoryComputational

PhysicsData Mining Experiment

2 Computational Pillars

Mathematical Modeling

Mathematical Modeling

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

Computing

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.

Computational Physics is an active field

Journals and Magazines…

APS, EPS, IPS…

Scientific Papers On-line at arXiv.org

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

Reference

Reference

Reference