The Finite Element Method for Problems in Physics

课程

英语

39 时

来源

来自www.coursera.org

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13 序列
等级中级

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课程详情

教学大纲

Week 1 - 1
This unit is an introduction to a simple one-dimensional problem that can be solved by the finite element method.
Week 2 - 2
In this unit you will be introduced to the approximate, or finite-dimensional, weak form for the one-dimensional problem.
Week 3 - 3
In this unit, you will write the finite-dimensional weak form in a matrix-vector form. You also will be introduced to coding in the deal.ii framework.
Week 4 - 4
This unit develops further details on boundary conditions, higher-order basis functions, and numerical quadrature. You also will learn about the templates for the first coding assignment.
Week 5 - 5
This unit outlines the mathematical analysis of the finite element method.
Week 6 - 6
This unit develops an alternate derivation of the weak form, which is applicable to certain physical problems.
Week 7 - 7
In this unit, we develop the finite element method for three-dimensional scalar problems, such as the heat conduction or mass diffusion problems.
Week 8 - 8
In this unit, you will complete some details of the three-dimensional formulation that depend on the choice of basis functions, as well as be introduced to the second coding assignment.
Week 9 - 9
In this unit, we take a detour to study the two-dimensional formulation for scalar problems, such as the steady state heat or diffusion equations.
Week 10 - 10
This unit introduces the problem of three-dimensional, linearized elasticity at steady state, and also develops the finite element method for this problem. Aspects of the code templates are also examined.
Week 11 - 11
In this unit, we study the unsteady heat conduction, or mass diffusion, problem, as well as its finite element formulation.
Week 12 - 12
In this unit we study the problem of elastodynamics, and its finite element formulation.
Week 13 - 113
This is a wrap-up, with suggestions for future study.

先决条件

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讲师

Krishna Garikipati, Ph.D.
Professor of Mechanical Engineering, College of Engineering - Professor of Mathematics, College of Literature, Science and the Arts