Schedule Optimisation for Interactive Parallel Structure Simulations

Introduction

Computational effort required for the interactive parallel simulation of a structure under loading usually does not allow for results to be gained rapidly. Further, custom decomposition techniques, as in the case of long structures such as thigh bones, typically hinder the efficient exploitation of the underlying computing power. For the algebraic equations, gained by the p-version Finite Element Method (p-FEM) describing the behaviour of one such structure, K ( u = d with K the system stiffness matrix, u the nodal displacements, and d all accumulated forces, often, due to the poor condition numbers, sophisticated iterative solvers fail to be efficient. As it is pointed out in [1, 3], applying hierarchical concepts, based on a nested dissection approach (i. e. recursive domain decomposition technique based on Schur complements, the de-facto standard of most domain decomposition approaches), allow for both the design of sophisticated direct solvers as well as for advanced parallelisation strategies, both of which are indispensable within interactive applications. Our main goal is the development of an efficient load balancing strategy for the existing structure simulation of the bone stresses with p-FEM organised via octrees as described in [2].