Getting Started with BEM (Boundary Element Method)

• Basic knowledge of vector calculus
• Understanding of ordinary and partial differential equations
• Understanding of complex variables
• Programming experience in any language

The BEM (Boundary Element Method) is a numerical computational method and design technique for solving a range of engineering and physical problems. BEM is a promising alternative to FEM (Finite Element Method) as it bypasses the need for a 3D finite element mesh of an entire space.

In this instructor-led, live training, participants will learn the theory and benefits of using BEM as they apply BEM techniques to solving engineering design problems related to complex three dimensional structures. The mathematical concepts behind BEM are explained and applied as coding exercises throughout the training.

Audience

• Developers
• Engineers

Format of the course

• Part lecture, part discussion, exercises and heavy hands-on practice

Introduction

• Boundary Elements vs Finite Elements

How Boundary Elements Integrate with Computer Aided Engineering (CAE) and Integrated Engineering Software

Continuous Elements, Discontinuous Elements and Surface Discretization

Versatility through Mesh Regeneration

Case study: Discretization of a Crankshaft

Setting up the Development Environment

Overview of BEM's Mathematical Foundations

Two-dimensional Laplace's Equation -- Solving a Simple Boundary Value Problem

Discontinuous Linear Elements -- Improving Approximations

Two-dimensional Helmholtz Type Equation -- Extending the Analysis

Two-dimensional Diffusion Equation

Green's Functions for Potential Problems

Analyzing Three-dimensional Problems

Analyzing Problems with Stress and Flux Concentrations

Analyzing Torsion, Diffusion, Seepage, Fluid Flow and Electrostatics

Combination with Finite Elements and the Hybrid Method

The Importance of Clean Code

Increasing Computational Performance (Parallel and Vector Computing)

Closing Remarks