A discontinuous Galerkin discretization for second order elliptic equations with discontinuous coefficients in 2-D is considered. The domain of interest Omega is assumed to be a union of polygonal substructures Omega(...
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ISBN:
(纸本)9783642113031
A discontinuous Galerkin discretization for second order elliptic equations with discontinuous coefficients in 2-D is considered. The domain of interest Omega is assumed to be a union of polygonal substructures Omega(i) of size O(H-i). We allow this substructure decomposition to be geometrically nonconforming. Inside each substructure Omega(i), a conforming finite element space associated to a triangulation T-hi (Omega(i)) is introduced. To handle the nonmatching meshes across partial derivative Omega(i), a discontinuous Galerkin discretization is considered. In this paper additive Neumann-Neumann Schwarz methods are designed and analyzed. Under natural assumptions on the coefficients and on the mesh sizes across partial derivative Omega(i), a condition number estimate C(1 + max(i) log H-i/h(i))(2) is established with C independent of h(i), H-i, h(i)/h(j), and the jumps of the coefficients. The method is well suited for parallel computations and can be straightforwardly extended to three dimensional problems. Numerical results, which are not included in this paper, confirm the theoretical results.
In this paper, we study preconditioning techniques for both H(grad) and H(curl) problems. For an H(grad) elliptic problem discretized by high-order finite elements with a hierachical basis of k-th order, we design and...
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ISBN:
(纸本)9783642113031
In this paper, we study preconditioning techniques for both H(grad) and H(curl) problems. For an H(grad) elliptic problem discretized by high-order finite elements with a hierachical basis of k-th order, we design and analyse an parallel AMG preconditioner based on a two-level method and a block Gauss-Seidel smoothing technique. For an H(curl) elliptic problem discretized by high-order edge finite elements, we design a parallel solver based on an auxiliary space preconditioner. Numerical experiments show that the number of iteration for the corresponding PCG methods does not depend on the mesh size, and depend weakly on the order of the finite element space and jumps of the coefficients.
In electromagnetism, a surface composed of a homogeneous planar substrate on a perfectly reflecting plane can be modelled by boundary layer method as a plane which satisfies surface boundary conditions with high order...
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For an initial-boundary value problem for a singularly perturbed parabolic reaction-diffusion equation on a composed domain, a conservative flux difference scheme on flux piecewise-uniform grids is constructed whose s...
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ISBN:
(纸本)9783642196645
For an initial-boundary value problem for a singularly perturbed parabolic reaction-diffusion equation on a composed domain, a conservative flux difference scheme on flux piecewise-uniform grids is constructed whose solution and also normalized diffusion flux converge (in the maximum norm) independent of the perturbation parameters at the rate O(N-2 In-2 N + N-0(-1)).
A direct solver for large scale sparse linear system of equations is presented in this paper. As a direct solver, this method is among the most efficient direct solvers available so far with flop count as O(n logn) in...
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ISBN:
(纸本)9783642113031
A direct solver for large scale sparse linear system of equations is presented in this paper. As a direct solver, this method is among the most efficient direct solvers available so far with flop count as O(n logn) in one-dimensional situations and O(n(3/2)) in second dimensional situation. This method has advantages over the existing fast solvers in which it can be used to handle more general situations, both well-conditioned or ill-conditioned systems;more importantly, it is a very stable solver and a naturally parallel procedure! Numerical experiments are presented to demonstrate the efficiency and stability of this algorithm.
In this paper, we examine a singularly perturbed convection-diffusion problem where the coefficients are smooth, but the solution contains an interior layer, generated from the fact that the initial condition contains...
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ISBN:
(数字)9783642196652
ISBN:
(纸本)9783642196645
In this paper, we examine a singularly perturbed convection-diffusion problem where the coefficients are smooth, but the solution contains an interior layer, generated from the fact that the initial condition contains an internal layer.
The use of Dirichlet-to-Neumann operators as transmission conditions is known to yield optimal Schwarz methods that converge in a finite number of iterations when the subdomain decomposition has tree-like connectivity...
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ISBN:
(纸本)9783642113031
The use of Dirichlet-to-Neumann operators as transmission conditions is known to yield optimal Schwarz methods that converge in a finite number of iterations when the subdomain decomposition has tree-like connectivity. However, it remains an open problem whether it is possible to construct a finitely terminating algorithm for arbitrary decompositions. In this article, we construct a Schwarz method that converges in exactly two steps for any decomposition into subdomains with minimal overlap. In this method, every subdomain must communicate with all other subdomains, but only data along subdomain boundaries need to be exchanged.
The upstream non linear interaction at high Reynolds number in a channel with local or global wall distortion is considered. Three methods are used to study the anticipated fluid response to the distal disturbance. &#...
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Our objective is to develop efficient parallel algorithms for reactive transport equations, which appear in problems related to the numerical simulation of geological CO2 storage. We present in this paper a new class ...
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When a problem is posed on an unbounded domain, the domain needs to be truncated in order to perform computations, and the pole condition is a new technique developed over the last few years for this purpose. The subj...
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