DEPENDENCIES OF PARALLEL SPARSE ITERATIVE LINEAR SOLVER METHODS ON MATRIX CONDITIONING ON UNSTRUCTURED FINITE ELEMENT MESHES

Iterative methods are widely used for solving sparse linear systems of equations and eigenvalue problems. Their performances are relevant to the conditioning of the linear systems. This work explores factors which affects the conditioning of the discretized system, including material heterogeneity, different constitutive characteristics and element sizes, and reveals the dependencies among solvers performance and the conditioning of linear systems. Results show that multiple materials can alter the eigenvalue distributions significantly, while lowering Young's modulus results in higher condition numbers but has less effects on the spectral scope, additionally, there is a approximately reciprocal square linear relation between element size and condition numbers. These entangled effects along with the chosen preconditioners render that there is no simple monotonic increasing dependency among condition numbers and solving time, except with specific conditions. It is hoped that this work will provide more understanding of the iterative sparse linear solver behavior used in similar structural problems.