PRECONDITIONING FOR THE p-VERSION BOUNDARY ELEMENT METHOD IN THREE DIMENSIONS WITH TRIANGULAR ELEMENTS
نویسندگان
چکیده
منابع مشابه
PRECONDITIONING FOR THE p-VERSION BOUNDARY ELEMENT METHOD IN THREE DIMENSIONS WITH TRIANGULAR ELEMENTS
A preconditioning algorithm is developed in this paper for the iterative solution of the linear system of equations resulting from the p-version boundary element approximation of the three dimensional integral equation with hypersingular operators. The preconditioner is derived by first making the nodal and side basis functions locally orthogonal to the element internal bases, and then by decou...
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This paper presents a exible approach to domain decomposition preconditioning for problems expressed in terms of local stiiness matrices of subdomains. Evaluation of the preconditioner requires fully parallelizable local computations and the solution of a global auxiliary problem with few variables per subdomain. Convergence factors can be bounded using properties of the local stiiness matrices...
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We prove an a priori error estimate for the hp-version of the boundary element method with hypersingular operators on piecewise plane open or closed surfaces. The underlying meshes are supposed to be quasi-uniform. The solutions of problems on polyhedral or piecewise plane open surfaces exhibit typical singularities which limit the convergence rate of the boundary element method. On closed surf...
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Already very early Prof. Oleg Zienkiewicz pointed to potential advantages of using higher order instead of low order shape functions for the finite element method [1]. The p-version as a systematic extension process of the finite element method leaves the mesh unchanged and increases the polynomial degree of the shape functions locally or globally [5]. It has turned out to be a very efficient d...
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For a plane polygonal domain Q and a corresponding (general) triangulation we define classes of functions pmix, v) which are polynomials on each triangle and which are in C^'CQ) and also belong to the Sobolev space ^""^'(n). Approximation theoretic properties are proved concerning these functions. These results are then applied to the approximate solution of arbitrary-order elliptic boundary va...
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2004
ISSN: 0304-9914
DOI: 10.4134/jkms.2004.41.2.345