Download Applications and Types for Physics Based Models - Special Topics | CS 4803 and more Study notes Computer Science in PDF only on Docsity! Introduction to Modeling and Simulation Applications and Types for Physics-based Models Outline Why use continuous modeling? Types of continuous modeling Processes of continuous modeling An example problem Brief review of numerical differentiation Analytical and Numerical Solutions Analytical problems are best are solving linear problems E.g., solving Newton’s second law of motion Many physical problems are nonlinear, so must resort to numerical solutions Nevertheless, analytical solutions are often valuable. Why? Verification of numerical solutions Gaining insights Examples where analytical solutions do not work Three-body problem Types of Simulations Particle simulations Monte Carlo Simulations Continuum physics Finite-difference Finite-element Hybrid simulations Particle Methods Bodies are simulated as point mass Particles interact with each other Numbers of particles may be small (e.g., solar system ~10) or large (molecular dynamics 103-107, galaxies 1011, or plasma systems 1024) It can be challenging to simulate interaction of large number of particles Use of super-particles to reduce amount of particles Particle-in-cell (PIC) method to reduce interactions Periodic structures to reduce domain size molecular dynamics galaxy Continuous Physics Using Finite-Element Method Alternative to finite-difference methods Especially for problems with complex boundary, where domain is discretized by meshes Method determines values at nodes Traditionally used in steady-state problems, but also often used for diffusion or wave motion Hybrid Simulations Combination of different types Combination of particles and Monte Carlo Brownian motion Combination of finite-difference and particles Particle in cells Hybrid discrete-event and continuous modeling E.g., multi-scale simulations Process of Solving Continuous Problems Modeling Numerical solutions Analysis of data, visualization Verification and validation Often iterative process Verification & validation are very important aspect Many sources of errors: program bugs, numerical errors (round- off and truncation errors) and modeling errors Compare against analytical solution Compare against experimentation “Sanity checking”, convergence study, consistent story
