Notre Dame courses
ame30251: computational methods (aut24)ame20251: computational methods (aut23)
ame70732: computational fluid dynamics (aut21, aut23)
ame60714: advanced numerical methods (aut20, spr23)
ame40541/60541: finite element methods (spr20, spr21, spr22, aut22, spr24)
ame50541: finite element methods (spr19)
AME40541/60541: Finite Element Methods
Lecture
Location: B34/36 Geddes Hall
Meeting time: MWF 1:00pm - 1:50pm
Recitation: Tu 4:30pm-5:30pm
Office Hours
Matthew J. Zahr, 300B Cushing Hall, MW 1:50p-3p, Th 5p-7p, F 10a-12p, 2p-5p
Tianci Huang, virtual, MTh 4p-6p
Xuemin Liu, virtual, MTh 4p-6p
Description
The finite element method is the industry-standard for solving a range of thermal, structural, and fluid flow problems that commonly arise in engineering practice and research. Commercial software is well-suited for solving such problems; however, having a fundamental understanding of the underlying methods is crucial to effectively use the software, develop methods/code tailored to the particular problems they face, or undertake cutting-edge research. This course introduces the fundamental concepts of finite element methods with applications to structural analysis, heat flow, fluid mechanics, and multiphysics problems. It covers the basic topics of linear and nonlinear finite element technology including weak formulations and error analysis, domain discretization on structured and unstructured meshes, assembly of global equations, the isoparametric concept, essential and natural boundary conditions, numerical quadrature, variational crimes, and the structure of a finite element program. Throughout the course, students will build their own finite element code that will be used to investigate fundamental properties of finite element methods. In addition, the course makes use of commercial software to explore more advanced capabilities, validate their own code, and gain experience with software commonly used in engineering industry.
Course Details
Course syllabus (pdf)
Lecture slides
Introduction to AME40541/60541 (pdf)
Course notes
Ch 1: Direct stiffness method (pdf)
Ch 2: Mathematical preliminaries (pdf)
Ch 3: Weighted residual methods (pdf)
Ch 4: Finite element method, 1D (pdf)
Ch 5: Variational formulation (pdf)
Ch 6: Finite element method, nD (pdf)
Ch 7: Finite element method, nonlinear (pdf)
Homework
Homework 1 (pdf, comsol_heat2d) - due 2/8
Homework 2 (pdf) - due 2/15
Homework 3 (pdf, code) - due 2/22
Homework 4 (pdf) - due 3/1
Homework 5 (pdf) - due 3/8
Homework 6 (pdf, code) - due 3/15
Homework 7 (pdf, code) - due 3/30
Homework 8 (pdf, code) - due TBD