The Complex Variable Boundary Element Method

1. Front Matter

   Pages N2-XI

   PDF

2. Flow Processes and Mathematical Models

   • Theodore V. Hromadka II

   Pages 1-10

3. A Review of Complex Variable Theory

   • Theodore V. Hromadka II

   Pages 11-45

4. Mathematical Development of the Complex Variable Boundary Element Method

   • Theodore V. Hromadka II

   Pages 46-100

5. The Complex Variable Boundary Element Method

   • Theodore V. Hromadka II

   Pages 101-161

6. Reducing CVBEM Approximation Relative Error

   • Theodore V. Hromadka II

   Pages 162-204

7. Advanced Topics

   • Theodore V. Hromadka II

   Pages 205-241

8. Back Matter

   Pages 242-245

   PDF

The Complex Variable Boundary Element Method or CVBEM is a generalization of the Cauchy integral formula into a boundary integral equation method or BIEM. This generalization allows an immediate and extremely valuable transfer of the modeling techniques used in real variable boundary integral equation methods (or boundary element methods) to the CVBEM. Consequently, modeling techniques for dissimilar materials, anisotropic materials, and time advancement, can be directly applied without modification to the CVBEM. An extremely useful feature offered by the CVBEM is that the pro­ duced approximation functions are analytic within the domain enclosed by the problem boundary and, therefore, exactly satisfy the two-dimensional Laplace equation throughout the problem domain. Another feature of the CVBEM is the integrations of the boundary integrals along each boundary element are solved exactly without the need for numerical integration. Additionally, the error analysis of the CVBEM approximation functions is workable by the easy-to-understand concept of relative error. A sophistication of the relative error analysis is the generation of an approximative boundary upon which the CVBEM approximation function exactly solves the boundary conditions of the boundary value problem' (of the Laplace equation), and the goodness of approximation is easily seen as a closeness-of-fit between the approximative and true problem boundaries.

• Boundary
• Fluid
• Numerical integration
• Taylor series
• boundary element method
• complex number
• constant
• form
• integral
• integral equation
• model
• modeling
• potential theory
• theorem
• variable
• complexity

• Department of Civil Engineering, University of California, Irvine, USA

  Theodore V. Hromadka

Policies and ethics