Interactive Boundary Element Analysis for Engineering Design

Abstract

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.