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291.
Julien Dompierre Marie‐Gabrielle Vallet Yves Bourgault Michel Fortin Wagdi G. Habashi 《国际流体数值方法杂志》2002,39(8):675-702
The present paper is the third article in a three‐part series on anisotropic mesh adaptation and its application to two‐ and three‐dimensional, structured and unstructured meshes. This third paper concerns the application of the full adaptation methodology to 2‐D unstructured meshes, including all four mesh modification strategies presented in Part I, i.e. refinement/coarsening, edge swapping and node movement. The mesh adaptation procedure is validated through a careful monitoring of a single adaptation step and of the solution–adaptation loop. Independence from the initial mesh and from the flow solver is illustrated. The efficiency of the overall methodology is investigated on relevant laminar and turbulent flow benchmarks. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
292.
Tin-Lam Toh 《Journal of Mathematical Analysis and Applications》2003,280(1):133-147
In this note we shall prove that the stochastic integral with respect to a semimartingale can be defined by Riemann's approach. However in this approach we use non-uniform meshes instead of the usual uniform meshes. 相似文献
293.
Dominik Steup 《International Journal of Infrared and Millimeter Waves》1992,13(11):1767-1779
Considering recent ozon problems in the upper atmosphere the measuring technique in the spectral range of about some hundred GHz gains in importance increasingly. Ozon concentration is measured by high sensitive radiometers consisting of several quasioptical components. A tunable bandpass filter represents a versatile component in such a test assembly. The bandpass filter is realized as interferometer and can be adapted to its respective application by individual tuning of its coupling links. Metallic meshes of different aperture size are used for injection and feedback of the electromagnetic wave. A stepper motor control serves for the integration in an automatic measurement setup. The construction principles of the interferometer are summarized. An analysis of the component by means of plane wave theory is extended to a theory of diffraction. Finally the theoretical approach is verified on an application as single-sideband filter comparing the measured results with the computed values of the simulation. 相似文献
294.
295.
This paper contains error estimates for covolume discretizations of Maxwell's equations in three space dimensions. Several estimates are proved. First, an estimate for a semi-discrete scheme is given. Second, the estimate is extended to cover the classical interlaced time marching technique. Third, some of our unstructured mesh results are specialized to rectangular meshes, both uniform and nonuniform. By means of some additional analysis it is shown that the spatial convergence rate is one order higher than for the unstructured case.
296.
Dynamic moving interfaces are central to many scientific, engineering, and graphics applications. In this paper, we introduce a novel method for moving surface meshes, called the face offsetting method, based on a generalized Huygens’ principle. Our method operates directly on a Lagrangian surface mesh, without requiring an Eulerian volume mesh. Unlike traditional Lagrangian methods, which move each vertex directly along an approximate normal or user-specified direction, our method propagates faces and then reconstructs vertices through an eigenvalue analysis locally at each vertex to resolve normal and tangential motion of the interface simultaneously. The method also includes techniques for ensuring the integrity of the surface as it evolves. Face offsetting provides a unified framework for various dynamic interface problems and delivers accurate physical solutions even in the presence of singularities and large curvatures. We present the theoretical foundation of our method, and also demonstrate its accuracy, efficiency, and flexibility for a number of benchmark problems and a real-world application. 相似文献
297.
《Applied Mathematical Modelling》2014,38(5-6):1612-1621
Nonlinear reaction–diffusion systems are often employed in mathematical modeling for pattern formation. Most of the work to date has been concerned within one-dimensional or rectangular domains. However, it is recognised that in most applications multidimensional complex geometrical domains are typically more important. In this paper we solve reaction–diffusion systems by combining direct discontinuous Galerkin (DDG) finite element methods with implicit integration factor (IIF) time integration method, on triangular meshes. This allows us solve the nonlinear algebraic systems on an element-by-element bases with significant gains in computational time. Numerical solutions of two reaction–diffusion systems, the well-studied Schnakenberg model and chloride–iodide–malonic acid (CIMA) reactive model, are presented to demonstrate effects of various domain geometries on the resulting biological patterns. Our numerical results are in good agreement with other numerical and analytical results, and with experimental results. 相似文献
298.
Lin Mu Junping Wang Xiu Ye 《Numerical Methods for Partial Differential Equations》2014,30(3):1003-1029
A new weak Galerkin (WG) finite element method is introduced and analyzed in this article for the biharmonic equation in its primary form. This method is highly robust and flexible in the element construction by using discontinuous piecewise polynomials on general finite element partitions consisting of polygons or polyhedra of arbitrary shape. The resulting WG finite element formulation is symmetric, positive definite, and parameter‐free. Optimal order error estimates in a discrete H2 norm is established for the corresponding WG finite element solutions. Error estimates in the usual L2 norm are also derived, yielding a suboptimal order of convergence for the lowest order element and an optimal order of convergence for all high order of elements. Numerical results are presented to confirm the theory of convergence under suitable regularity assumptions. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1003–1029, 2014 相似文献
299.
Sebastian Franz Hans‐Görg Roos Andreas Wachtel 《Numerical Methods for Partial Differential Equations》2014,30(3):838-861
We analyze the convergence of a continuous interior penalty (CIP) method for a singularly perturbed fourth‐order elliptic problem on a layer‐adapted mesh. On this anisotropic mesh, we prove under reasonable assumptions uniform convergence of almost order k ? 1 for finite elements of degree k ≥ 2. This result is of better order than the known robust result on standard meshes. A by‐product of our analysis is an analytic lower bound for the penalty of the symmetric CIP method. Finally, our convergence result is verified numerically. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 838–861, 2014 相似文献
300.