1,720,996 research outputs found
BEM coupling with the FEM fictitious domain approach for the solution of the exterior Poisson problem and of wave scattering by rotating rigid bodies
Full text linkWe consider two exterior model problems in two dimensions: the Poisson equation and the problem of
waves scattered by rotating rigid bodies. The exterior domain is the R^2 complement of a bounded rigid
obstacle, subject to a rotation in the time-dependent case. By using a fictitious domain approach, we
artificially extend the solution to the whole of R^2. Then, we propose and study a finite element–boundary
element coupling method for the solution of the problem in a finite computational domain, delimited by an
artificial boundary B. The transmission conditions between the interior and exterior domains are imposed
on B by a boundary integral equation coupled first to the Poisson, and then to the wave equation, these
being defined in the interior domain. The Dirichlet conditions on the boundary of the physical obstacle
are enforced weakly by means of Lagrange multipliers. The main advantage of this approach is that the
finite element mesh can be chosen independently of the geometry of the obstacle. Moreover, in the timedependent
case, the proposed method allows the use of a given fixed mesh, thus avoiding the complexity
of constructing at each time step a new finite element computational mesh.
For the Poisson problem we obtain convergence results when the space discretization is performed
by standard finite elements in the interior domain and by a Galerkin boundary element method on B.
For the wave equation, we perform a full space discretization by finite elements, coupled with a Crank–
Nicolson time-stepping scheme. On the boundary B, the boundary element method and a convolution
quadrature based on the backward differentiation method of order 2 are used.We present numerical results
for nontrivial data, which validate the proposed numerical approach. In the wave equation case, these also
include rotating obstacles and external sources
Analysis of the MortarMethod with Approximate Integration: the Effect of Cross-Points
No full textPubbl. IAN n.1298-P
On some equivalent Sobolev spaces: analysis of injection bounds by wavelet schemes
No full textPubbl. IMATI n.14-P
A new boundary element integration strategy for retarded potential boundary integral equations
Full text linkWe consider the retarded potential boundary integral equation, arising from the 3D Dirichlet exterior wave equation problem. For its numerical solution we use compactly supported temporal basis functions in time and a standard collocation method in space. Since the accurate computation of the integrals involved in the numerical scheme is a key issue for the numerical stability, we propose a new efficient and competitive quadrature strategy. We compare this approach with the one that uses the Lubich time convolution quadrature, and show pros and cons of both methods
An exact non reflecting boundary condition for 2D time-dependent wave equation problems
Full text linkExact non-reflecting boundary condition for 3D time-dependent multiple scattering-multiple source problems
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