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ABC_PML

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PML comparison
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  ABS and PMLMartin J. GanderDomainTruncation HistoryExample TBS and ABS ConstructionApplication: ABCs PML HistoricalStretched-CoordinatePML Pole Condition MeaningApproximations MathematicalEquivalences With PMLWith ABCNumericalExperimentsOptimization of   s  0 Conclusions Are Absorbing Boundary Conditionsand Perfectly Matched LayersReally so Different ? Martin J. Gander  martin.gander@unige.ch University of Geneva RICAM, November 2011Joint work with Achim Sch¨adle  ABS and PMLMartin J. GanderDomainTruncation HistoryExample TBS and ABS ConstructionApplication: ABCs PML HistoricalStretched-CoordinatePML Pole Condition MeaningApproximations MathematicalEquivalences With PMLWith ABCNumericalExperimentsOptimization of   s  0 Conclusions History of Absorbing Boundary Conditions Engquist and Majda (1977): Wave Propagation:  “Inpractical calculations, it is often essential to introduce artificialboundaries to limit the area of computation.Unfortunately [transparent boundary conditions] necessarily haveto be non-local in both space and time and thus are not useful forpractical calculations” Bayliss Turkel (1980): Wave-Like Equations:  “In thenumerical computation of hyperbolic equations it is not practicalto use infinite domains. Instead, one truncates the domain with anartificial boundary“ Halpern (Wave Propagation 1982, Diffusion 1987): “...one often introduces artificial boundaries with boundaryconditions chosen so that the problem one gets is well-posed andthe solution is ’as close as possible’ to that of the srcinalproblem”  ABS and PMLMartin J. GanderDomainTruncation HistoryExample TBS and ABS ConstructionApplication: ABCs PML HistoricalStretched-CoordinatePML Pole Condition MeaningApproximations MathematicalEquivalences With PMLWith ABCNumericalExperimentsOptimization of   s  0 Conclusions Truncation of an Infinite Computational Domain Airbus A340 in approach over a cityTruncation of the unbounded domain using ◮  A transparent (or exact) boundary condition (TBC) oran absorbing (or inexact) boundary condition (ABC) ◮  A perfectly matched layer (PML)  ABS and PMLMartin J. GanderDomainTruncation HistoryExample TBS and ABS ConstructionApplication: ABCs PML HistoricalStretched-CoordinatePML Pole Condition MeaningApproximations MathematicalEquivalences With PMLWith ABCNumericalExperimentsOptimization of   s  0 Conclusions Interest for Domain Decomposition Methods Computation performed with an optimized Schwarz methodon 16 subdomainsAn optimized Schwarz method with two-sided Robintransmission conditions for the Helmholtz equation (G,Halpern and Magoules, 2006)
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