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

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