A Parallel Gaussian Elimination for Jacobian Calculation in Magnetotelluric Occam Inversion Algorithm

A parallel Gaussian elimination algorithm for Jacobian matrix calculation is designed to accelerate the MT Occam algorithm. The gaussd progress calculates the column matrix which is build by receivers' data. The parallel gaussd process is based on the original Gaussian parallel algorithm. The back substitution equation has been transformed to increase the elements in parallel area. By storing the primary row of coefficient matrix and RJ matrix to shared memory, memory accessing time is reduced. The parallel gaussd is implemented in CUDA FORTRAN. Using the gauss and gaussd parallel algorithms together can reduce the data transform between GPU and host. The highest speedup of parallel gaussd is 22. It greatly improves the efficiency of Jacobian matrix calculation in MT Occam algorithm.