scholarly journals A general framework for substructuring‐based domain decomposition methods for models having nonlocal interactions

2021 ◽  
Author(s):  
Giacomo Capodaglio ◽  
Marta D'Elia ◽  
Max Gunzburger ◽  
Pavel Bochev ◽  
Manuel Klar ◽  
...  
Keyword(s):  
Domain Decomposition ◽  
General Framework ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Nonlocal Interactions

scholarly journals A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions.

2020 ◽  
Author(s):  
Marta D'Elia ◽  
Pavel Bochev ◽  
Max Gunzburger ◽  
Giacomo Capodaglio ◽  
Manuel Klar ◽  
...  
Keyword(s):  
Domain Decomposition ◽  
General Framework ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Nonlocal Interactions

scholarly journals A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions.

2020 ◽  
Author(s):  
Marta D'Elia ◽  
Pavel Bochev ◽  
Max Gunzburger ◽  
Giacomo Capodaglio ◽  
Manuel Klar ◽  
...  
Keyword(s):  
Domain Decomposition ◽  
General Framework ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Nonlocal Interactions

scholarly journals Exponentially convergent non overlapping domain decomposition methods for the Helmholtz equation

2020 ◽  
Vol 54 (3) ◽  
pp. 775-810 ◽  
Author(s):  
Francis Collino ◽  
Patrick Joly ◽  
Matthieu Lecouvez
Keyword(s):  
Domain Decomposition ◽  
General Framework ◽  
Domain Decomposition Method ◽  
Integral Operators ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Convergent Method ◽  
Non Local ◽  
Overlapping Domain Decomposition ◽  
Well Posed

In this paper, we develop in a general framework a non overlapping Domain Decomposition Method that is proven to be well-posed and converges exponentially fast, provided that specific transmission operators are used. These operators are necessarily non local and we provide a class of such operators in the form of integral operators. To reduce the numerical cost of these integral operators, we show that a truncation process can be applied that preserves all the properties leading to an exponentially fast convergent method. A modal analysis is performed on a separable geometry to illustrate the theoretical properties of the method and we exhibit an optimization process to further reduce the convergence rate of the algorithm.

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