期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 78, 期 2, 页码 459-482出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2018.09.045
关键词
Transmission problem; Mortar method; Lagrange multiplier; Advection-diffusion; Elastodynamics; Hessenberg index-1 DAE
资金
- U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research [DE-SC-0000230927]
- Coupling Approaches for Next-Generation Architectures (CANGA) project - United States Department of Energy's Office of Science under the Scientific Discovery through Advanced Computing (SciDAC)
- Coupling Approaches for Next-Generation Architectures (CANGA) project - Laboratory Directed Research and Development program at Sandia National Laboratories
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. 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. (C) 2018 Elsevier Ltd. All rights reserved.
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