Explicit synchronous partitioned algorithms for interface problems based on Lagrange multipliers

Peterson, Kara; Bochev, Pavel; Kuberry, Paul

doi:10.1016/j.camwa.2018.09.045

Title: Explicit synchronous partitioned algorithms for interface problems based on Lagrange multipliers

Journal Article · Mon Jul 01 00:00:00 EDT 2019 · Computers and Mathematics with Applications (Oxford)

DOI:https://doi.org/10.1016/j.camwa.2018.09.045· OSTI ID:1989708

Peterson, Kara; Bochev, Pavel;

Traditional explicit partitioned schemes exchange boundary conditions between subdomains and can be related to iterative solution methods for the coupled problem. As a result, these schemes may require multiple subdomain solves, acceleration techniques, or optimized transmission conditions to achieve sufficient accuracy and/or stability. We present a new synchronous partitioned method derived from a well-posed mixed finite element formulation of the coupled problem. We transform the resulting Differential Algebraic Equation (DAE) to a Hessenberg index-1 form in which the algebraic equation defines the Lagrange multiplier as an implicit function of the states. Using this fact we eliminate the multiplier and reduce the DAE to a system of explicit ODEs for the states. Explicit time integration both discretizes this system in time and decouples its equations. As a result, the temporal accuracy and stability of our formulation are governed solely by the accuracy and stability of the explicit scheme employed and are not subject to additional stability considerations as in traditional partitioned schemes. Here, we establish sufficient conditions for the formulation to be well-posed and prove that classical mortar finite elements on the interface are a stable choice for the Lagrange multiplier. We show that in this case the condition number of the Schur complement involved in the elimination of the multiplier is bounded by a constant. The paper concludes with numerical examples illustrating the approach for two different interface problems.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: SC-0000230927; AC04-94AL85000

OSTI ID:: 1989708

Alternate ID(s):: OSTI ID: 1492351; OSTI ID: 1636882

Report Number(s):: SAND-2018-14135J; S0898122118305637; PII: S0898122118305637

Journal Information:: Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Vol. 78 Journal Issue: 2; ISSN 0898-1221

Publisher:: ElsevierCopyright Statement

Country of Publication:: United Kingdom

Language:: English

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Cited by: 9 works

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