Fast multimodel finite-difference controlled-source electromagnetic simulations based on a Schur complement approach

Jaysaval, Piyoosh; Shantsev, D. V.; Ryhove, Sébastien de la Kethulle de

doi:10.1190/geo2014-0043.1

Cited by 40 publications

(11 citation statements)

References 36 publications

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“…In all simulations the system matrix was generated using the finite-difference modelling code presented in Jaysaval et al (2014). The simulations were carried out on either (1) the CALMIP supercomputer EOS (https://www.calmip.univ-toulouse.fr/), which is a BULLx DLC system composed of 612 computing nodes, each composed of two Intel Ivybridge processors with 10 cores (total 12 240 cores) running at 2.8 GHz per node and 64 GB/node, or (2) a computer FARAD with 16-core Intel Xeon CPU E5-2690 processors running at 2.90 GHz and 264 GB memory.…”

Section: R E S U Lt Smentioning

confidence: 99%

“…In the padded regions the gridding was severely non-uniform and followed the rules described by Jaysaval et al (2014), where the air was discretized with 15 cells and the other boundaries with 7 cells. Apart from the padded regions, we used finite-difference grids that were uniform in all three directions.…”

Section: Models and System Matricesmentioning

confidence: 99%

“…Therefore the application of direct solvers to 3-D problems has traditionally been considered computationally too demanding. However, recent advances in sparse matrix-factorization packages, for example, MUMPS (Amestoy et al 2001(Amestoy et al , 2006, PARDISO (Schenk & Gärtner 2004), SuperLU (Li & Demmel 2003), UMFPACK (Davis 2004) and WSMP (Gupta & Avron 2000), along with the availability of modern parallel computing environments, have created the necessary conditions to attract interest in direct solvers in the case of 3-D EM problems of moderate size, see for example, Blome et al (2009), Streich (2009), da Silva et al (2012, Puzyrev et al (2016) and Jaysaval et al (2014).…”

Section: Introductionmentioning

confidence: 99%

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Large-scale 3-D EM modelling with a Block Low-Rank multifrontal direct solver

Shantsev

Jaysaval

Ryhove³

et al. 2017

Geophysical Journal International

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S U M M A R YWe put forward the idea of using a Block Low-Rank (BLR) multifrontal direct solver to efficiently solve the linear systems of equations arising from a finite-difference discretization of the frequency-domain Maxwell equations for 3-D electromagnetic (EM) problems. The solver uses a low-rank representation for the off-diagonal blocks of the intermediate dense matrices arising in the multifrontal method to reduce the computational load. A numerical threshold, the so-called BLR threshold, controlling the accuracy of low-rank representations was optimized by balancing errors in the computed EM fields against savings in floating point operations (flops). Simulations were carried out over large-scale 3-D resistivity models representing typical scenarios for marine controlled-source EM surveys, and in particular the SEG SEAM model which contains an irregular salt body. The flop count, size of factor matrices and elapsed run time for matrix factorization are reduced dramatically by using BLR representations and can go down to, respectively, 10, 30 and 40 per cent of their full-rank values for our largest system with N = 20.6 million unknowns. The reductions are almost independent of the number of MPI tasks and threads at least up to 90 × 10 = 900 cores. The BLR savings increase for larger systems, which reduces the factorization flop complexity from O(N 2 ) for the full-rank solver to O(N m ) with m = 1.4-1.6. The BLR savings are significantly larger for deep-water environments that exclude the highly resistive air layer from the computational domain. A study in a scenario where simulations are required at multiple source locations shows that the BLR solver can become competitive in comparison to iterative solvers as an engine for 3-D controlled-source electromagnetic Gauss-Newton inversion that requires forward modelling for a few thousand right-hand sides.

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Section: R E S U Lt Smentioning

confidence: 99%

Section: Models and System Matricesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Large-scale 3-D EM modelling with a Block Low-Rank multifrontal direct solver

Shantsev

Jaysaval

Ryhove³

et al. 2017

Geophysical Journal International

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“…This is especially important for EM inversion requiring sequential solution of multiple forward problems. Recently, significant advances have been made in developing the direct solvers for forward EM problems (e.g., Grayver et al 2013;Jaysaval et al 2014). However, the direct solvers still impose challenging memory requirements for large-scale 3D problems, which makes the iterative solvers more attractive in geophysical applications.…”

Section: Introductionmentioning

confidence: 99%

Contraction preconditioner in finite-difference electromagnetic modeling

Yavich

Zhdanov

2016

SEG Technical Program Expanded Abstracts 2016

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This paper introduces a novel approach to constructing an effective preconditioner for finite-difference (FD) electromagnetic modeling in geophysical applications based on an FD contraction operator, similar to one developed for integral equation formulation of Maxwell's equation. The contraction properties of this operator were established using an FD analog of the energy equality for the anomalous electromagnetic field. We have also developed the formulas for an estimation of the condition number of the system of FD equations preconditioned using the introduced FD contraction operator. The numerical examples illustrate the practical effectiveness of the developed method for modeling 3D marine controlledsource electromagnetic data.

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“…Direct solvers have tradition- ally been considered to be too computationally demanding for 3D problems compared to iterative solvers. However, gradual advancement of direct-solution algorithms, along with the availability of resources for parallel computation, makes it possible to apply these algorithms for solving large-scale 3D problems very efficiently (Streich, 2009;da Silva et al, 2012;Yang and Oldenburg, 2012;Grayver et al, 2013;Schwarzbach and Haber, 2013;Jaysaval et al, 2014). In particular, in the case of multisource problems such as marine CSEM, the direct solvers may perform more efficiently than the iterative solvers because the direct solvers reuse the decomposed system matrix for multiple sources whereas the iterative solvers need to solve the problem for each source separately (Chung et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

A hybrid finite-difference and integral-equation method for modeling and inversion of marine controlled-source electromagnetic data

et al. 2016

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One of the major problems in the modeling and inversion of marine controlled-source electromagnetic (CSEM) data is related to the need for accurate representation of very complex geoelectrical models typical for marine environment. At the same time, the corresponding forward-modeling algorithms should be powerful and fast enough to be suitable for repeated use in hundreds of iterations of the inversion and for multiple transmitter/receiver positions. To this end, we have developed a novel 3D modeling and inversion approach, which combines the advantages of the finitedifference (FD) and integral-equation (IE) methods. In the framework of this approach, we have solved Maxwell's equations for anomalous electric fields using the FD approximation on a staggered grid. Once the unknown electric fields in the computation domain of the FD method are computed, the electric and magnetic fields at the receivers are calculated using the IE method with the corresponding Green's tensor for the background conductivity model. This approach makes it possible to compute the fields at the receivers accurately without the need of very fine FD discretization in the vicinity of the receivers and sources and without the need for numerical differentiation and interpolation. We have also developed an algorithm for 3D inversion based on the hybrid FD-IE method. In the case of the marine CSEM problem with multiple transmitters and receivers, the forward modeling and the Fréchet derivative calculations are very time consuming and require using large memory to store the intermediate results.To overcome those problems, we have applied the moving sensitivity domain approach to our inversion. A case study for the 3D inversion of towed streamer EM data collected by PGS over the Troll field in the North Sea demonstrated the effectiveness of the developed hybrid method.

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Fast multimodel finite-difference controlled-source electromagnetic simulations based on a Schur complement approach

Cited by 40 publications

References 36 publications

Large-scale 3-D EM modelling with a Block Low-Rank multifrontal direct solver

Large-scale 3-D EM modelling with a Block Low-Rank multifrontal direct solver

Contraction preconditioner in finite-difference electromagnetic modeling

A hybrid finite-difference and integral-equation method for modeling and inversion of marine controlled-source electromagnetic data

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