An implementation of the QMR method based on coupled two-term recurrences
SIAM Journal on Scientific Computing
Fast simulation of 3D electromagnetic problems using potentials
Journal of Computational Physics
Fast Finite Volume Simulation of 3D Electromagnetic Problems with Highly Discontinuous Coefficients
SIAM Journal on Scientific Computing
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
FEMSTER: An object-oriented class library of high-order discrete differential forms
ACM Transactions on Mathematical Software (TOMS)
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
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An essential element for computational hypothesis testing, data inversion and experiment design for electromagnetic geophysics is a robust forward solver, capable of easily and quickly evaluating the electromagnetic response of arbitrary geologic structure. The usefulness of such a solver hinges on the balance among competing desires like ease of use, speed of forward calculation, scalability to large problems or compute clusters, parsimonious use of memory access, accuracy and by necessity, the ability to faithfully accommodate a broad range of geologic scenarios over extremes in length scale and frequency content. This is indeed a tall order. The present study addresses recent progress toward the development of a forward solver with these properties. Based on the Lorenz-gauged Helmholtz decomposition, a new finite volume solution over Cartesian model domains endowed with complex-valued electrical properties is shown to be stable over the frequency range 10^-^2-10^1^0Hz and range 10^-^3-10^5m in length scale. Benchmark examples are drawn from magnetotellurics, exploration geophysics, geotechnical mapping and laboratory-scale analysis, showing excellent agreement with reference analytic solutions. Computational efficiency is achieved through use of a matrix-free implementation of the quasi-minimum-residual (QMR) iterative solver, which eliminates explicit storage of finite volume matrix elements in favor of ''on the fly'' computation as needed by the iterative Krylov sequence. Further efficiency is achieved through sparse coupling matrices between the vector and scalar potentials whose non-zero elements arise only in those parts of the model domain where the conductivity gradient is non-zero. Multi-thread parallelization in the QMR solver through OpenMP pragmas is used to reduce the computational cost of its most expensive step: the single matrix-vector product at each iteration. High-level MPI communicators farm independent processes to available compute nodes for simultaneous computation of multi-frequency or multi-transmitter responses.