Feasibility study of GeoFEM for solving 100 million DOF problems

GeoFEM is a parallel FEM code to analyze solid earth. This report describes large-scaled structural analysis features of the code. One of the purposes for GeoFEM/Tiger version consists in 100 million degree of freedoms (DOF) analysis by parallelized FEM. Here, we discuss the problem to be solved by GeoFEM, the method to enable such a large-scaled structural analysis and its visibility. GeoFEM adopts domain decomposition method (DDM), assuming distributed memory type parallel computers and it solves all degrees of freedom by iterative method such as conjugate gradient. At this stage, the largest linear elastic problem solved by \GeoFEM" is more than 100M (100,000,000) degree of freedoms with reasonable scalability on 1,000 PEs Hitachi SR2201 at University of Tokyo. Introduction GeoFEM[1],[2] is a parallel FEM system to analyze solid earth. The structure analysis subsystem of GeoFEM deals with solidus behavior of the earth. The solid earth analyses to be solved by GeoFEM system are lithospheric plate motions and earthquake wave propagation problems. The former is a static problem, and it must be considered strong nonlinearity because of geographical complexity. The latter is a dynamic problem including massive time series calculation. We have to handle large scale and complex nonlinearity to solve such a kind of problems. However for the rst order approximation, we can analyze those problems by linear system. Although the latter dynamic analysis is usually adopted explicit method, we can apply static techniques excluding time integration scheme. Therefore we discuss here only for large scaled linear analysis, and exclude complexity or dynamic problem. Large scale plate motion analysis According to the plate tectonics theory, the earth is covered with lithospheric plates, which move over the low viscous asthenosphere layer. And main earthly behaviors like earthquake arise from plate boundaries. Especially around the Japanese archipelago, the Eurasia plate, the Paci c Sea plate and the Philippine Sea plate are