Numerical Methods, Multigrid

Mulder, W.A.

doi:10.1007/978-3-030-10475-7_153-1

Cited by 1 publication

(1 citation statement)

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“…The standard multigrid approach fails for severe stretching or strong anisotropy, for which known improvements such as line-relaxation and semicoarsening (Jönsthövel et al 2006) are implemented, with a non-standard Cholesky decomposition to speed up the computation (Mulder et al 2008). One of the big advantages of the multigrid method is that it scales linearly (optimal) with the grid size in both CPU and RAM usage (Mulder 2020). This makes it feasible to run even big models on standard computers, without the need for big clusters.…”

Section: E T H O D O L O G Ymentioning

confidence: 99%

Fast Fourier transform of electromagnetic data for computationally expensive kernels

Werthmüller

Mulder

Slob

2021

Geophysical Journal International

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SUMMARY 3-D controlled-source electromagnetic data are often computed directly in the domain of interest, either in the frequency domain or in the time domain. Computing it in one domain and transforming it via a Fourier transform to the other domain is a viable alternative. It requires the evaluation of many responses in the computational domain if standard Fourier transforms are used. This can make it prohibitively expensive if the kernel is time-consuming as is the case in 3-D electromagnetic modelling. The speed of modelling obtained through such a transform is defined by three key points: solver, method and implementation of the Fourier transform, and gridding. The faster the solver, the faster modelling will be. It is important that the solver is robust over a wide range of values (frequencies or times). The method should require as few kernel evaluations as possible while remaining robust. As the frequency and time ranges span many orders of magnitude, the required values are ideally equally spaced on a logarithmic scale. The proposed fast method uses either the digital linear filter method or the logarithmic fast Fourier transform together with a careful selection of evaluation points and interpolation. In frequency-to-time domain tests this methodology requires typically 15–20 frequencies to cover a wide range of offsets. The gridding should be frequency- or time-dependent, which is accomplished by making it a function of skin depth. Optimizing for the least number of required cells should be combined with optimizing for computational speed. Looking carefully at these points resulted in much smaller computation times with speedup factors of ten or more over previous methods. A computation in one domain followed by transformation can therefore be an alternative to computation in the other domain domain if the required evaluation points and the corresponding grids are carefully chosen.

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Section: E T H O D O L O G Ymentioning

confidence: 99%