Time efficient 3-D electromagnetic modeling on massively parallel computers

A numerical modeling algorithm has been developed to simulate the electromagnetic response of a three dimensional earth to a dipole source for frequencies ranging from 100 to 100MHz. The numerical problem is formulated in terms of a frequency domain--modified vector Helmholtz equation for the scattered electric fields. The resulting differential equation is approximated using a staggered finite difference grid which results in a linear system of equations for which the matrix is sparse and complex symmetric. The system of equations is solved using a preconditioned quasi-minimum-residual method. Dirichlet boundary conditions are employed at the edges of the mesh by setting the tangential electric fields equal to zero. At frequencies less than 1MHz, normal grid stretching is employed to mitigate unwanted reflections off the grid boundaries. For frequencies greater than this, absorbing boundary conditions must be employed by making the stretching parameters of the modified vector Helmholtz equation complex which introduces loss at the boundaries. To allow for faster calculation of realistic models, the original serial version of the code has been modified to run on a massively parallel architecture. This modification involves three distinct tasks; (1) mapping the finite difference stencil to a processor stencil which allows for the necessary information to be exchanged between processors that contain adjacent nodes in the model, (2) determining the most efficient method to input the model which is accomplished by dividing the input into ``global`` and ``local`` data and then reading the two sets in differently, and (3) deciding how to output the data which is an inherently nonparallel process