Abstract
This paper deals with interface operators in boundary value problems: how to define them, which is their meaning in both mathematical and physical sense, how to use them to derive numerical approximations based on domain decomposition approaches. When matching partial differential equations set in adjacent subregions of a domain Ω of ℝn, the interface operators ensure the fulfillement of transmission conditions between the different solutions. From the mathematical side, they make it possible to reduce the overall boundary value problem into a subproblem depending solely on the trace of the solution upon the interface. Once the solution of such a problem is available, the original solution can be reconstructed through the solution of independent boundary value problems within each subregion. The above independency feature is very likely behind the increasing interest for the use in the recent years of interface operators in scientific computing. Indeed, the subdomain approach yields a problem to be solved for the interface gridvalues only, then a family of reduced problems are left to solve simultaneously, hopefully by a multiprocessor architecture.
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© 1991 Kluwer Academic Publishers
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Quarteroni, A., Valli, A. (1991). Theory and Application of Steklov-Poincaré Operators for Boundary-Value Problems. In: Spigler, R. (eds) Applied and Industrial Mathematics. Mathematics and Its Applications, vol 56. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1908-2_14
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DOI: https://doi.org/10.1007/978-94-009-1908-2_14
Publisher Name: Springer, Dordrecht
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