| 1. |
- Massing, André, et al.
(författare)
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A Nitsche-Based Cut Finite Element Method for a Fluid--Structure Interaction Problem
- 2015
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Ingår i: Communications in Applied Mathematics and Computational Science. - : Mathematical Sciences Publishers. - 1559-3940 .- 2157-5452. ; 10:2, s. 97-120
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Tidskriftsartikel (refereegranskat)abstract
- We present a new composite mesh finite element method for fluid-structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh that is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation that allows us to establish stability and optimal-order a priori error estimates. We consider here a steady state fluid-structure interaction problem where a hyperelastic structure interacts with a viscous fluid modeled by the Stokes equations. We evaluate an iterative solution procedure based on splitting and present three-dimensional numerical examples.
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| 2. |
- Massing, Andre, et al.
(författare)
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A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem
- 2014
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Ingår i: Journal of Scientific Computing. - : Springer Science and Business Media LLC. - 0885-7474 .- 1573-7691. ; 61:3, s. 604-628
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Tidskriftsartikel (refereegranskat)abstract
- We present a novel finite element method for the Stokes problem on fictitious domains. We prove inf-sup stability, optimal order convergence and uniform boundedness of the condition number of the discrete system. The finite element formulation is based on a stabilized Nitsche method with ghost penalties for the velocity and pressure to obtain stability in the presence of small cut elements. We demonstrate for the first time the applicability of the Nitsche fictitious domain method to three-dimensional Stokes problems. We further discuss a general, flexible and freely available implementation of the method and present numerical examples supporting the theoretical results.
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| 3. |
- Massing, Andre, et al.
(författare)
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A stabilized Nitsche overlapping mesh method for the Stokes problem
- 2014
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Ingår i: Numerische Mathematik. - : Springer Science and Business Media LLC. - 0029-599X .- 0945-3245. ; 128:1, s. 73-101
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Tidskriftsartikel (refereegranskat)abstract
- We develop a Nitsche-based formulation for a general class of stabilized finite element methods for the Stokes problem posed on a pair of overlapping, non-matching meshes. By extending the least-squares stabilization to the overlap region, we prove that the method is stable, consistent, and optimally convergent. To avoid an ill-conditioned linear algebra system, the scheme is augmented by a least-squares term measuring the discontinuity of the solution in the overlap region of the two meshes. As a consequence, we may prove an estimate for the condition number of the resulting stiffness matrix that is independent of the location of the interface. Finally, we present numerical examples in three spatial dimensions illustrating and confirming the theoretical results.
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| 4. |
- Massing, Andre, et al.
(författare)
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Efficient implementation of finite element methods on nonmatching and overlapping meshes in three dimensions
- 2013
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Ingår i: SIAM Journal of Scientific Computing. - 1064-8275 .- 1095-7197 .- 1095-7200. ; 35:1, s. C23-C47
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Tidskriftsartikel (refereegranskat)abstract
- In recent years, a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on nonmatching or overlapping meshes. Examples of such methods are the fictitious domain method, the extended finite element method, and Nitsche's method. In all these methods, integrals must be computed over cut cells or subsimplices, which is challenging to implement, especially in three space dimensions. In this note, we address the main challenges of such an implementation and demonstrate good performance of a fully general code for automatic detection of mesh intersections and integration over cut cells and subsimplices. As a canonical example of an overlapping mesh method, we consider Nitsche's method, which we apply to Poisson's equation and a linear elastic problem. © 2013 Society for Industrial and Applied Mathematics.
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