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# lec1 - Introduction to Simulation Lecture 1 Example...

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Introduction to Simulation - Lecture 1 Thanks to Deepak Ramaswamy, Michal Rewienski, Luca Daniel, Shihhsien Kuo and Karen Veroy Example Problems and Basic Equations Jacob White

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Outline Uses For Simulation Engineering Design Virtual Environments Model Verification Course Philosophy Example Problems Power distribution on an Integrated Circuit Load bearing on a space frame Temperature distribution in a package
Circuit Analysis Equations Current-voltage relations for circuit elements (resistors, capacitors, transistors, inductors), current balance equations Recent Developments Matrix-Implicit Krylov Subspace methods

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Electromagnetic Analysis of Packages Equations Maxwell’s Partial Differential Equations Recent Developments Fast Solvers for Integral Formulations
Structural Analysis of Automobiles Equations Force-displacement relationships for mechanical elements (plates, beams, shells) and sum of forces = 0. Partial Differential Equations of Continuum Mechanics Recent Developments Meshless Methods, Iterative methods, Automatic Error Control

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Drag Force Analysis of Aircraft Equations Navier-Stokes Partial Differential Equations. Recent Developments Multigrid Methods for Unstructured Grids
Engine Thermal Analysis Equations The Poisson Partial Differential Equation. Recent Developments Fast Integral Equation Solvers, Monte-Carlo Methods

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Micromachine Device Performance Analysis Equations Elastomechanics, Electrostatics, Stokes Flow. Recent Developments Fast Integral Equation Solvers, Matrix-Implicit Multi-level Newton Methods for coupled domain problems.
Stock Option Pricing for Hedge Funds Equations Black-Scholes Partial Differential Equation Recent Developments Financial Service Companies are hiring engineers, mathematicians and physicists. t Stock Price Option Price

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1 Virtual Environments for Computer Games Equations Multibody Dynamics, elastic collision equations. Recent Developments Multirate integration methods, parallel simulation
1 Virtual Surgery Equations Partial Differential Equations of Elastomechanics Recent Developments Parallel Computing, Fast methods

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1 Biomolecule Electrostatic Optimization Equations The Poisson Partial Differential Equation. Recent Developments Matrix-Implicit Iterative Methods, Fast Integral Equation Solvers Ligand (drug molecule) + + - - - - + + + Receptor (protein molecule) + + + + + + - - - Ecm protein
1 The Computer Simulation Senario Problem too complicated for hand analysis Make Sense? No Solve a Simplified Problem Toss out some Terms “Macromodel” Yes Simulate using a canned routine, a friend’s advice, or a recipe book D R O P C L A S S Develop Understanding of Computational complexity Way too slow Only works sometimes Develop Understanding of Convergence Issues Anxiety Works!

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