Boundary Element Method

Course Numbers: 20-MECH-7504;   Spring Semester

Instructor: Dr. Yijun Liu, Professor of Mechanical Engineering

Contents of the Lectures

Chapter 1. Introduction

  • Lecture 1. Introduction to the BEM
  • Lecture 2. An Example - Bending of a Simple Beam
  • Lecture 3. Review of the Mathematical Principles
  • Homework #1

Chapter 2. Potential Problem

  • Lecture 1. Governing Equation and the Physical Problems; the Fundamental Solutions (2-D and 3-D)
  • Lecture 2. Boundary Integral Equation (BIE) Formulation
  • Lecture 3. Discretization of the BIE Using Constant Boundary Elements
  • Lecture 4. Higher Order Boundary Elements
  • Lecture 5. Multi-Region Problems; Infinite Domain Problems
  • Lecture 6. Domain Integrals; Indirect BIE/BEM Formulations
  • Lecture 7. Programming for the BEM
  • Lecture 8. Applications of the BEM for Potential Problems
  • Homework #2; Homework #3
  • BEM Program for 2-D Potential Problems (include the PC executable file; Fortran source code and an input file)

Chapter 3. Fast Multipole BEM for Potential Problem

  • Lecture 1. Introduction FMM
  • Lecture 2. FMM for 2-D Potential Problems
  • Lecture 3. Programming of Fast Multipole BEM for 2-D Potential Problem
  • Lecture 4. Applications
  • Midterm Project Assignment

Chapter 4. Elastostatic Problem

  • Lecture 1. Governing Equations and the Fundamental Solutions
  • Lecture 2. BIE Formulation
  • Lecture 3. Fast multipole BEM for Elastostatic Problem
  • Lecture 4. Applications in Stress Analysis and Fracture Mechanics Problems
  • Homework #4

Chapter 5. Stokes Flow Problem

  • Lecture 1. Governing Equations and the Fundamental Solutions
  • Lecture 2. BIE Formulation
  • Lecture 3. Fast multipole BEM for Stokes Flow Problem
  • Lecture 4. Applications
  • Homework #5

Chapter 6. Acoustic Problem

  • Lecture 1. Basic Equations in Acoustics and the BIE Formulation
  • Lecture 2. Advanced BIE Formulations in Acoustics
  • Lecture 3. Fast multipole BEM for Acoustic Problem
  • Lecture 4. Applications in Structural Acoustics
  • Homework #6
  • Final Project

Chapter 7. Further Research Topics

  • Lecture 1. Recent development in the BEM
  • Presentation of the Final Project - I
  • Presentation of the Final Project - II

 Contact Info

E-mail:   Yijun.Liu@uc.edu
Tel.
:         (513) 556-4607 (Voice),    (513) 556-3390 (Fax)
S-mail:    Mechanical Engineering, University of Cincinnati, P.O. Box 210072, Cincinnati, OH 45221-0072


  1997-2013 Yijun Liu, University of Cincinnati

Last updated April 26, 2013.