Scalable Preconditioners for Structure Preserving Discretizations of Maxwell Equations in First Order Form

Journal Article · Tue May 01 00:00:00 EDT 2018 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/17M1135827· OSTI ID:1441484

Phillips, Edward Geoffrey ^[1]; Shadid, John N. ^[1]; Cyr, Eric C. ^[1]

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1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Here, we report multiple physical time-scales can arise in electromagnetic simulations when dissipative effects are introduced through boundary conditions, when currents follow external time-scales, and when material parameters vary spatially. In such scenarios, the time-scales of interest may be much slower than the fastest time-scales supported by the Maxwell equations, therefore making implicit time integration an efficient approach. The use of implicit temporal discretizations results in linear systems in which fast time-scales, which severely constrain the stability of an explicit method, can manifest as so-called stiff modes. This study proposes a new block preconditioner for structure preserving (also termed physics compatible) discretizations of the Maxwell equations in first order form. The intent of the preconditioner is to enable the efficient solution of multiple-time-scale Maxwell type systems. An additional benefit of the developed preconditioner is that it requires only a traditional multigrid method for its subsolves and compares well against alternative approaches that rely on specialized edge-based multigrid routines that may not be readily available. Lastly, results demonstrate parallel scalability at large electromagnetic wave CFL numbers on a variety of test problems.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
• Grant/Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1441484
• Report Number(s): SAND--2018-4332J; 662668
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 3 Vol. 40; ISSN 1064-8275
• Publisher: SIAM
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Maxwell equations
compatible discretization
preconditioning