CEE 598 BEM

Boundary  Element Methods

Fall 2004

• Course Outline

• Textbooks on BEM

• IABEM 2002 Symposium (handout) (link) 

• BEM 24                            (handout) (link)

• EABE                               (handout) (link)

• BEC                                 (link)

• "Error analysis and adaptivity in the Boundary element and related methods"    

    Subrata Mukherjee, 

    Professor, Department of Theoretical and Applied Mechanics, Cornell University (abstract) 

 Handouts will be provided throughout the semester.  In case you need another copy, a pdf file containing the handout will be placed here.  

•  In the Efficiency and Accuracy of the BEM and the FEM    
• Powerpoint Presentation
• Boundary Elements and Symmetry
• BEAN Demo 
• Table of Green's Function
• Mathematical Preliminaries
• A Finite Elastic Body with a Curved Crack loaded in Anti-plane Shear
• An Integral Equation Solution of the Torsion Problem
• The Sum of H_ik in BEM
• Multizone Problems
• Program for the Poisson's equation
• Nonlinear Problems
• Singular Integrals
• Some identities for fundamental solution
• Logarithmic Gaussian Quadrature Parameters
• Crack problem for nonhomogeneous materials (singularity substraction)
• A general algorithm for Numerical Solution of HBIE
• HBIE: Some Applications in Acoustic and Elastic Wave Scattering
• Hypersingular residual error estimation
• A weakly singular form of the HBIE applied to 3-D acoustic wave problems
• The performance of spheroidal infinite elements (FEM)
• Boundary element method implementation for 3D Transient Elastodynamics
• Nodal sensitivities as error estimates in computational mechanics
• Design Sensitivity Analysis of Solids Using BEM
• Boundary Integral Equations for Recovery of Design Sensitivities in Shape Opimization
• Boundary Integral Equation Method for Shape Optimization for Elastic Structures
• Meshless BNM 1
• Meshless BNM 2
• Hypersingular integrals
• Heat Conduction in FGMs
• Boundary Elements for exterior problems.

• Assignment #1
• Homework Solution # 1
• Modeling with educational program BEAN
• Modeling with commercial software BEASY

• Project # 1  
• Project # 2                                                   

• "Multi-region and Frictionless Contact Problems in BEM" by Spandan Maiti.
• "Coupling of Finite Cloud Method with the Boundary Element Method" by Gang Li 
• "Post-Processing the Spectral Method to Obtain Off-Plane Quantities"    by  M. Scot Breitenfeld.
• "Mixed-Mode Fracture Analysis via Coupling the Finite Element Method and the Symmetric Galerkin Method". by Jeong-Ho Kim
• "A Domain Decomposition Based Two-Level Newton Scheme to Couple FEM and BEM" by Deepak Kulkarni.
• "Three Dimensional Boundary Element Analysis Program for Laplace’s Equation." by Chang Joon Lee.
• "Application of 3-dimensional Potential Theory to Electrostatic Simulation using Boundary Element Method." by  Vaishali Shrivastava.

(Papers discussed in the class but not posted on the web)

• Regularization Techniques:  Tanaka, M., Sladek, V., and Sladek, J. (1994). Regularization techniques applied to boundary element methods. ASME Applied Mechanics Reviews, 47:457-499.

• Hypersingular Boundary Integral Equations:  Krishnasamy G., Rizzo F.J. , Rudolphi T.J., Hypersingular Boundary Integral Equations:  Their occurrence, interpretation, regularization and computation.  In: Advanced Dynamic Analysis by Boundary Element Methods, Development in Boundary Element Methods-7 Series, Editors: Banerjee P.K. and Kobayashi S., Elsevier Science Publishers Ltd. pp. 207-252. 1992. 

 Commercial 

• BEASY - Computational Mechanics Inc.

• GPBEST - Boundary Element Software Technology (BEST) Corporation.

• COMET/Acoustics - Collins & Aikman

• AutoBEM - Coyote Systems.

 Educational 

•  BEAN (Boundary Element ANalysis)

• BENET  -   Boundary Element Resources Network

The support from the Computational Science and Engineering (CSE) program at UIUC is gratefully acknowledged.