The tensor-train mimetic finite difference method for three-dimensional Maxwell’s wave propagation equations

Manzini, G.; Truong, P. M. D.; Vuchkov, R.; Alexandrov, B.

doi:10.1016/j.matcom.2023.03.026

Title: The tensor-train mimetic finite difference method for three-dimensional Maxwell’s wave propagation equations

Journal Article · Tue Aug 01 00:00:00 EDT 2023 · Mathematics and Computers in Simulation

DOI:https://doi.org/10.1016/j.matcom.2023.03.026· OSTI ID:1967529

;

; Vuchkov, R.;

Coupling the mimetic finite difference method with the tensor-train format results in a very effective method for low-rank numerical approximations of the solutions of the time-dependent Maxwell wave propagation equations in three dimensions. To this end, we discretize the curl operators on the primal/dual tensor product grid complex and we couple the space discretization with a staggered-in-time second-order accurate time-marching scheme. The resulting solver is accurate to the second order in time and space, and still compatible, so that the approximation of the magnetic flux field has zero discrete divergence with a discrepancy close to the machine precision level. Our approach is not limited to the second-order of accuracy. We can devise higher-order formulations in space through suitable extensions of the tensor-train stencil to compute the derivatives of the mimetic differential operators. Employing the tensor-train format improves the solver performance by orders of magnitude in terms of CPU time and memory storage. A final set of numerical experiments confirms this expectation.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001; 20190020DR; 20210485ER; NA0003525

OSTI ID:: 1967529

Alternate ID(s):: OSTI ID: 1968208; OSTI ID: 2311532

Report Number(s):: LA-UR-22-28983; SAND-2023-04299J; S0378475423001313; PII: S0378475423001313

Journal Information:: Mathematics and Computers in Simulation, Journal Name: Mathematics and Computers in Simulation Vol. 210 Journal Issue: C; ISSN 0378-4754

Publisher:: ElsevierCopyright Statement

Country of Publication:: Netherlands

Language:: English

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97 MATHEMATICS AND COMPUTING
mathematics
tensor-train format
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Maxwell's equations
partial differential equations

Title: The tensor-train mimetic finite difference method for three-dimensional Maxwell’s wave propagation equations

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