scholarly journals Adaptive anisotropic integration scheme for high-order fictitious domain methods: Application to thin structures

2018 ◽  
Vol 114 (8) ◽  
pp. 882-904 ◽  
Author(s):  
G. Legrain ◽  
N. Moës
Keyword(s):  
High Order ◽  
Fictitious Domain ◽  
Integration Scheme ◽  
Thin Structures ◽  
Fictitious Domain Methods

Fictitious Domain Methods for the Numerical Solution of Two-Dimensional Scattering Problems

1998 ◽  
Vol 145 (1) ◽  
pp. 89-109 ◽  
Author(s):  
Erkki Heikkola ◽  
Yuri A. Kuznetsov ◽  
Pekka Neittaanmäki ◽  
Jari Toivanen
Keyword(s):  
Numerical Solution ◽  
Fictitious Domain ◽  
Two Dimensional ◽  
Scattering Problems ◽  
Fictitious Domain Methods

scholarly journals Simulating water-entry/exit problems using Eulerian–Lagrangian and fully-Eulerian fictitious domain methods within the open-source IBAMR library

2020 ◽  
Vol 94 ◽  
pp. 101932 ◽  
Author(s):  
Amneet Pal Singh Bhalla ◽  
Nishant Nangia ◽  
Panagiotis Dafnakis ◽  
Giovanni Bracco ◽  
Giuliana Mattiazzo
Keyword(s):  
Open Source ◽  
Water Entry ◽  
Fictitious Domain ◽  
Fictitious Domain Methods ◽  
Exit Problems

NEW FICTITIOUS DOMAIN METHODS: FORMULATION AND ANALYSIS

2005 ◽  
Vol 15 (10) ◽  
pp. 1575-1594 ◽  
Author(s):  
IVO BABUŠKA ◽  
EUGENE G. PODNOS ◽  
GREGORY J. RODIN
Keyword(s):  
Model Problem ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Fictitious Domain ◽  
Element Mesh ◽  
Multiple Interfaces ◽  
Fictitious Domain Methods ◽  
The Cost

Two closely-related fictitious domain methods for solving problems involving multiple interfaces are introduced. Like other fictitious domain methods, the proposed methods simplify the task of finite element mesh generation and provide access to solvers that can take advantage of uniform structured grids. The proposed methods do not involve the Lagrange multipliers, which makes them quite different from existing fictitious domain methods. This difference leads to an advantageous form of the inf–sup condition, and allows one to avoid time-consuming integration over curvilinear surfaces. In principle, the proposed methods have the same rate of convergence as existing fictitious domain methods. Nevertheless it is shown that, at the cost of introducing additional unknowns, one can improve the quality of the solution near the interfaces. The methods are presented using a two-dimensional model problem formulated in the context of linearized theory of elasticity. The model problem is sufficient for presenting method details and mathematical foundations. Although the model problem is formulated in two dimensions and involves only one interface, there are no apparent conceptual difficulties to extending the methods to three dimensions and multiple interfaces. Further, it is possible to extend the methods to nonlinear problems involving multiple interfaces.

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