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Two-dimensional Domains (two-dimensional + domain)
Selected AbstractsA relation between the logarithmic capacity and the condition number of the BEM-matricesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2007W. Dijkstra Abstract We establish a relation between the logarithmic capacity of a two-dimensional domain and the solvability of the boundary integral equation for the Laplace problem on that domain. It is proved that when the logarithmic capacity is equal to one the boundary integral equation does not have a unique solution. A similar result is derived for the linear algebraic systems that appear in the boundary element method. As these systems are based on the boundary integral equation, no unique solution exists when the logarithmic capacity is equal to one. Hence, the system matrix is ill-conditioned. We give several examples to illustrate this and investigate the analogies between the Laplace problem with Dirichlet and mixed boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. [source] On the complexity of finding paths in a two-dimensional domain I: Shortest pathsMLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 6 2004Arthur W. Chou Abstract The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: (A) domains with polynomialtime computable boundaries, and (B) polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type (A) and type (B); and it has a polynomial-space lower bound for the domains of type (B), and has a #P lower bound for the domains of type (A). (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Preconditioning and a posteriori error estimates using h - and p -hierarchical finite elements with rectangular supportsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 5 2009I. Pultarová Abstract We show some of the properties of the algebraic multilevel iterative methods when the hierarchical bases of finite elements (FEs) with rectangular supports are used for solving the elliptic boundary value problems. In particular, we study two types of hierarchies; the so-called h - and p -hierarchical FE spaces on a two-dimensional domain. We compute uniform estimates of the strengthened Cauchy,Bunyakowski,Schwarz inequality constants for these spaces. Moreover, for diagonal blocks of the stiffness matrices corresponding to the fine spaces, the optimal preconditioning matrices can be found, which have tri- or five-diagonal forms for h - or p -refinements, respectively, after a certain reordering of the elements. As another use of the hierarchical bases, the a posteriori error estimates can be computed. We compare them in test examples for h - and p -hierarchical FEs with rectangular supports. Copyright © 2008 John Wiley & Sons, Ltd. [source] Semi-analytical elastostatic analysis of unbounded two-dimensional domainsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2002Andrew J. Deeks Abstract Unbounded plane stress and plane strain domains subjected to static loading undergo infinite displacements, even when the zero displacement boundary condition at infinity is enforced. However, the stress and strain fields are well behaved, and are of practical interest. This causes significant difficulty when analysis is attempted using displacement-based numerical methods, such as the finite-element method. To circumvent this difficulty problems of this nature are often changed subtly before analysis to limit the displacements to finite values. Such a process is unsatisfactory, as it distorts the solution in some way, and may lead to a stiffness matrix that is nearly singular. In this paper, the semi-analytical scaled boundary finite-element method is extended to permit the analysis of such problems without requiring any modification of the problem itself. This is possible because the governing differential equations are solved analytically in the radial direction. The displacement solutions so obtained include an infinite component, but relative motion between any two points in the unbounded domain can be computed accurately. No small arbitrary constants are introduced, no arbitrary truncation of the domain is performed, and no ill-conditioned matrices are inverted. Copyright © 2002 John Wiley & Sons, Ltd. [source] A new fast hybrid adaptive grid generation technique for arbitrary two-dimensional domainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2010Mohamed S. Ebeida Abstract This paper describes a new fast hybrid adaptive grid generation technique for arbitrary two-dimensional domains. This technique is based on a Cartesian background grid with square elements and quadtree decomposition. A new algorithm is introduced for the distribution of boundary points based on the curvature of the domain boundaries. The quadtree decomposition is governed either by the distribution of the boundary points or by a size function when a solution-based adaptive grid is desired. The resulting grid is quaddominant and ready for the application of finite element, multi-grid, or line-relaxation methods. All the internal angles in the final grid have a lower bound of 45° and an upper bound of 135°. Although our main interest is in grid generation for unsteady flow simulations, the technique presented in this paper can be employed in many other fields. Several application examples are provided to illustrate the main features of this new approach. Copyright © 2010 John Wiley & Sons, Ltd. [source] Guaranteed-quality triangular mesh generation for domains with curved boundariesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2002Charles Boivin Guaranteed-quality unstructured meshing algorithms facilitate the development of automatic meshing tools. However, these algorithms require domains discretized using a set of linear segments, leading to numerical errors in domains with curved boundaries. We introduce an extension of Ruppert's Delaunay refinement algorithm to two-dimensional domains with curved boundaries and prove that the same quality bounds apply with curved boundaries as with straight boundaries. We provide implementation details for two-dimensional boundary patches such as lines, circular arcs, cubic parametric curves, and interpolated splines. We present guaranteed-quality triangular meshes generated with curved boundaries, and propose solutions to some problems associated with the use of curved boundaries. Copyright © 2002 John Wiley & Sons, Ltd. [source] Different models for the polar nanodomain structure of PZN and other relaxor ferroelectricsJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3 2008T. R. Welberry Computer simulations have been carried out to test the recently proposed model for the nanodomain structure of relaxor ferroelectrics such as lead zinc niobate (PZN). In this recent model it was supposed that the polar nanodomains are three-dimensional, that the observed diffuse rods of scattering originate from the boundaries between domains and that the Pb displacements may be directed along , or . This is in marked contrast to a previously published model, which described the polar domains as thin plates with Pb displacements confined to the directions within the essentially two-dimensional domains. The present results confirm that and types of Pb displacement are viable possibilities, but the number of domain boundaries required to produce sufficiently strong diffuse rods of scattering means that individual domains cannot be described as three-dimensional and must still be relatively thin. The current work has been carried out with no direct involvement of the B -site cation ordering, which many workers assume is necessary to understand the formation of the polar nanodomains. While it may be true that the B -site cation distribution could provide an underlying perturbation field that might ultimately limit the extent of any polar domain, it is certainly not necessary to produce the observed scattering effects. [source] Minimal regularity of the solutions of some transmission problemsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2003D. Mercier We consider some transmission problems for the Laplace operator in two-dimensional domains. Our goal is to give minimal regularity of the solutions, better than H1, with or without conditions on the (positive) material constants. Under a monotonicity or quasi-monotonicity condition on the constants (or on the inverses according to the boundary conditions), we study the behaviour of the solution near vertex and near interior nodes and show in each case that the given regularity is sharp. Without condition we prove that the regularity near a corner is of the form H1+,, where , is a given bound depending on the material constants. Numerical examples are presented which confirm the sharpness of our lower bounds. Copyright © 2003 John Wiley & Sons, Ltd. [source] On the complexity of finding paths in a two-dimensional domain I: Shortest pathsMLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 6 2004Arthur W. Chou Abstract The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: (A) domains with polynomialtime computable boundaries, and (B) polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type (A) and type (B); and it has a polynomial-space lower bound for the domains of type (B), and has a #P lower bound for the domains of type (A). (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||