For a singularly perturbed convection-diffusion problem with exponential and characteristic boundary layers on the unit square a discretisation based on layer-adapted meshes is considered. The standard Galerkin method...
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ISBN:
(数字)9783642196652
ISBN:
(纸本)9783642196645
For a singularly perturbed convection-diffusion problem with exponential and characteristic boundary layers on the unit square a discretisation based on layer-adapted meshes is considered. The standard Galerkin method and the local projection scheme are analysed for a general class of higher order finite elements based on local polynomial spaces lying between P-p and Q(p) We will present two different interpolation operators for these spaces. The first one is based on values at vertices, weighted edge integrals and weighted cell integrals while the second one is based on point values only. The influence of the point distribution on the errors will be studied numerically. We show convergence of order p in the epsilon-weighted energy norm for both the Galerkin method and the local projection scheme. Furthermore, the local projection methods provides a supercloseness result of order p in local projection norm.
Multiple scattering of waves is one of the important research topics in scientific and industrial fields. A number of numerical methods have been developed to compute waves scattered by several obstacles, e.g., acoust...
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The Additive Schwarz Method with Harmonic Extension (ASH) was introduced by Cai and Sarkis (1999) as an efficient variant of the additive Schwarz method that converges faster and requires less communication. We show h...
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ISBN:
(纸本)9783642113031
The Additive Schwarz Method with Harmonic Extension (ASH) was introduced by Cai and Sarkis (1999) as an efficient variant of the additive Schwarz method that converges faster and requires less communication. We show how ASH, which is defined at the matrix level, can be reformulated as an iteration that bears a close resemblance to the parallel Schwarz method at the continuous level, provided that the decomposition of subdomains contains no cross points. In fact, the iterates of ASH are identical to the iterates of the discretized parallel Schwarz method outside the overlap, whereas inside the overlap they are linear combinations of previous Schwarz iterates. Thus, the two methods converge with the same asymptotic rate, unlike additive Schwarz, which fails to converge inside the overlap (Efstathiou & Gander 2007).
For a class of multilevel preconditioners based on non-nested meshes, we study numerically several selected prolongation and restriction operators. Robustness with respect to the mesh size and to jumps in the coeffici...
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ISBN:
(纸本)9783642113031
For a class of multilevel preconditioners based on non-nested meshes, we study numerically several selected prolongation and restriction operators. Robustness with respect to the mesh size and to jumps in the coefficients is demonstrated.
In this paper we study the application of Newton-Krylov-Schwarz method to fully implicit, fully coupled solution of a global shallow water model. In particular, we are interested in developing a scalable parallel solv...
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Two-dimensional laminar flow, at high Reynolds number Re, of an incompressible Newtonian fluid in a curved channel connected to two fitting tangent straight channels at its upstream and downstream extremities is consi...
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ISBN:
(纸本)9783642196645
Two-dimensional laminar flow, at high Reynolds number Re, of an incompressible Newtonian fluid in a curved channel connected to two fitting tangent straight channels at its upstream and downstream extremities is considered. The Successive Complementary Expansion Method (SCEM) is adopted. This method leads to an asymptotic reduced model called Global Interactive Boundary Layer (GIBL) which gives a uniformly valid approximate solution of the flow field in the whole domain. To explore the effect of the variable curvature on the flow field, the bend has an elliptical median line. The validity of the proposed GIBL model is confronted to the numerical solution of complete Navier-Stokes equations. This comparison includes the wall shear stress which is a very sensitive measure of the flow field. The GIBL results match very well the complete Navier stokes results for curvatures K-max up to 0.4, curvature variations vertical bar K'(max)vertical bar up to 0.7 and eccentricities e up to similar or equal to 0.943 in the whole geometrical domain. The upstream and downstream effects as well as the impact of the curvature discontinuities and the behaviour in the entire bend are well captured by the GIBL model.
The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from ...
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ISBN:
(纸本)9783642113031
The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method.
The coupling of different types of partial differential equations is an active field of research, since the need for such coupling arises in various applications. A first main area is the simulation of complex objects...
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