The Boundary Element Method in Acoustics

The boundary element method (BEM) is a powerful tool in computational acoustic analysis. The Boundary Element Method in Acoustics serves as an introduction to the BEM and its application to acoustic problems and goes on to complete the development of computational models. Software implementing the methods is available

Probabilistic boundary element method

The purpose of the Probabilistic Structural Analysis Method (PSAM) project is to develop structural analysis capabilities for the design analysis of advanced space propulsion system hardware. The boundary element method (BEM) is used as the basis of the Probabilistic Advanced Analysis Methods (PADAM) which is discussed. The probabilistic BEM code (PBEM) is used to obtain the structural response and sensitivity results to a set of random variables. As such, PBEM performs analogous to other structural analysis codes such as finite elements in the PSAM system. For linear problems, unlike the finite element method (FEM), the BEM governing equations are written at the boundary of the body only, thus, the method eliminates the need to model the volume of the body. However, for general body force problems, a direct condensation of the governing equations to the boundary of the body is not possible and therefore volume modeling is generally required

Composite micromechanical modeling using the boundary element method

The use of the boundary element method for analyzing composite micromechanical behavior is demonstrated. Stress-strain, heat conduction, and thermal expansion analyses are conducted using the boundary element computer code BEST-CMS, and the results obtained are compared to experimental observations, analytical calculations, and finite element analyses. For each of the analysis types, the boundary element results agree reasonably well with the results from the other methodologies, with explainable discrepancies. Overall, the boundary element method shows promise in providing an alternative method to analyze composite micromechanical behavior

COMGEN-BEM: Boundary element model generation for composite materials micromechanical analysis

Composite Model Generation-Boundary Element Method (COMGEN-BEM) is a program developed in PATRAN command language (PCL) which generates boundary element models of continuous fiber composites at the micromechanical (constituent) scale. Based on the entry of a few simple parameters such as fiber volume fraction and fiber diameter, the model geometry and boundary element model are generated. In addition, various mesh densities, material properties, fiber orientation angles, loads, and boundary conditions can be specified. The generated model can then be translated to a format consistent with a boundary element analysis code such as BEST-CMS

Adaptive boundary element methods with convergence rates

This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. The convergence rates are quasi-optimal in a certain sense under mild assumptions that are analogous to what is typically assumed in the theory of adaptive finite element methods. In particular, no saturation-type assumption is used. The main ingredients of the proof that constitute new findings are some results on a posteriori error estimates for boundary element methods, and an inverse-type inequality involving boundary integral operators on locally refined finite element spaces.Comment: 48 pages. A journal version. The previous version (v3) is a bit lengthie

Interactive boundary element analysis for engineering design.

Structural design of mechanical components is an iterative process that involves multiple stress analysis runs; this can be time consuming and expensive. Significant improvements in the eciency of this process can be made by increasing the level of interactivity. One approach is through real-time re-analysis of models with continuously updating geometry. Three primary areas need to be considered to accelerate the re-solution of boundary element problems. These are re-meshing the model, updating the boundary element system of equations and re-solution of the system. Once the initial model has been constructed and solved, the user may apply geometric perturbations to parts of the model. The re-meshing algorithm must accommodate these changes in geometry whilst retaining as much of the existing mesh as possible. This allows the majority of the previous boundary element system of equations to be re-used for the new analysis. For this problem, a GMRES solver has been shown to provide the fastest convergence rate. Further time savings can be made by preconditioning the updated system with the LU decomposition of the original system. Using these techniques, near real-time analysis can be achieved for 3D simulations; for 2D models such real-time performance has already been demonstrated