Hexahedral Element Mesh Research Articles

Porting a three-dimensional semiconductor device modelling program to the Intel iPSC/860 hypercube

EVEREST is a three-dimensional device modelling package used to study the electrical behaviour of semiconductor devices. A set of partial differential equations describing the current flow within the device is solved using a mixed mesh of tetrahedral and hexahedral elements. The highly non-linear nature of the equations requires that a flexible solution strategy be used to make the software robust and efficient. Within the solution process large sparse non-symmetric linear systems are solved using iterative solvers such as CGS with preconditioning. Run times of many hours or even days are required for realistic devices on current workstations. EVEREST consists of over 100 000 lines of Fortran and was developed for scalar architectures. The main aim of this work was to investigate how such an application could be adapted to run on the iPSC/860. A review of some of the possible parallelisation techniques is made. Most techniques for the parallel implementation of such mesh based calculations on MIMD machines involve a partitioning of the mesh. An extension of an algorithm due to Farhat has been implemented in a pre-processor to partition the device meshes used by EVEREST. Aspects of load balancing and the need to minimise the number of interface nodes in the decomposition are discussed. Some initial results using the partitioned mesh to perform the system matrix assembly are presented. Methods that could be used to implement a parallel preconditioned CGS solver on the iPSC/860 are reviewed and some performance estimates made using the results of certain BBS tests on this machine.

Model3—A three-dimensional mesh generator

A three-dimensional mesh generation program is presented. The program is based on the isoparametric superelement generation. These superelements consist of 20-node hexahedral elements specified by the user. Subdivision into a mesh of eight-node hexahedral elements is automatically performed according to the grading initially specified. A bandwidth reduction algorithm is incorporated in the program in order to optimize finite element core requirements. The program is written in FORTRAN and a glossary of terms and the program listing are provided.