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Interior Points (interior + point)

Distribution by Scientific Domains

Engineering	71%

Selected Abstracts

The boundary element method for solving the Laplace equation in two-dimensions with oblique derivative boundary conditions

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2007
D. Lesnic
Abstract In this communication, we extend the Neumann boundary conditions by adding a component containing the tangential derivative, hence producing oblique derivative boundary conditions. A variant of Green's formula is employed to translate the tangential derivative to the fundamental solution in the boundary element method (BEM). The two-dimensional steady-state heat conduction with the imposed oblique boundary condition has been tested in smooth, piecewise smooth and multiply connected domains in which the Laplace equation is the governing equation, producing results at the boundary in excellent agreement with the available analytical solutions. Convergence of the normal and tangential derivatives at the boundary is also achieved. The numerical boundary data are then used to successfully calculate the values of the solution at interior points again. The outlined test cases have been repeated with various boundary element meshes, indicating that the accuracy of the numerical results increases with increasing boundary discretization. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Axial symmetric elasticity analysis in non-homogeneous bodies under gravitational load by triple-reciprocity boundary element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009
Yoshihiro Ochiai
Abstract In general, internal cells are required to solve elasticity problems by involving a gravitational load in non-homogeneous bodies with variable mass density when using a conventional boundary element method (BEM). Then, the effect of mesh reduction is not achieved and one of the main merits of the BEM, which is the simplicity of data preparation, is lost. In this study, it is shown that the domain cells can be avoided by using the triple-reciprocity BEM formulation, where the density of domain integral is expressed in terms of other fields that are represented by boundary densities and/or source densities at isolated interior points. Utilizing the rotational symmetry, the triple-reciprocity BEM formulation is developed for axially symmetric elasticity problems in non-homogeneous bodies under gravitational force. A new computer program was developed and applied to solve several test problems. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Shape functions for polygonal domains with interior nodes

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2004
Elisabeth Anna Malsch
Abstract The presented formulation follows in a series of publications which outline a method for constructing test functions which satisfy essential edge conditions exactly. The method promises a complete solution, satisfying all of the requirements of a Ritz coordinate function. The influence of interior points on the domain solution is included in this construction. Similar to conformal bubble functions, the test functions are zero along the boundary and single valued only at the points they describe. Unlike the bubble function construction, the interior points can be located at any desired point in the domain. The resulting set of trial functions can satisfy the required global conditions including the exact reproduction of constant and linear fields. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Aerodynamic shape optimization on overset grids using the adjoint method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2010
Wei Liao
Abstract This paper deals with the use of the continuous adjoint equation for aerodynamic shape optimization of complex configurations with overset grids methods. While the use of overset grid eases the grid generation process, the non-trivial task of ensuring communication between overlapping grids needs careful attention. This need is effectively addressed by using a practically useful technique known as the implicit hole cutting (IHC) method. The method depends on a simple cell selection process based on the criterion of cell size, and all grid points including interior points and fringe points are treated indiscriminately in the computation of the flow field. This paper demonstrates the simplicity of the IHC method for the adjoint equation. Similar to the flow solver, the adjoint equations are solved on conventional point-matched and overlapped grids within a multi-block framework. Parallel computing with message passing interface is also used to improve the overall efficiency of the optimization process. The method is successfully demonstrated in several two- and a three-dimensional shape optimization cases for both external and internal flow problems. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Numerical boundary conditions for globally mass conservative methods to solve the shallow-water equations and applied to river flow

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2006
J. Burguete
Abstract A revision of some well-known discretization techniques for the numerical boundary conditions in 1D shallow-water flow models is presented. More recent options are also considered in the search for a fully conservative technique that is able to preserve the good properties of a conservative scheme used for the interior points. Two conservative numerical schemes are used as representatives of the families of explicit and implicit numerical methods. The implementation of the different boundary options to these schemes is compared by means of the simulation of several test cases with exact solution. The schemes with the global conservation boundary discretization are applied to the simulation of a real river flood wave leading to very satisfactory results. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A hybrid search combining interior point methods and metaheuristics for 0,1 programming

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 6 2002
Agnès Plateau
Our search deals with methods hybridizing interior point processes and metaheuristics for solving 0,1 linear programs. This paper shows how metaheuristics can take advantage of a sequence of interior points generated by an interior point method. After introducing our work field, we present our hybrid search which generates a diversified population. Next, we explain the whole method combining the solutions encountered in the previous phase through a path relinking template. Computational experiments are reported on 0,1 multiconstraint knapsack problems. [source]

On the size of the algebraic difference of two random Cantor sets

RANDOM STRUCTURES AND ALGORITHMS, Issue 2 2008
Michel Dekking
Abstract In this paper we consider some families of random Cantor sets on the line and investigate the question whether the condition that the sum of Hausdorff dimension is larger than one implies the existence of interior points in the difference set of two independent copies. We prove that this is the case for the so called Mandelbrot percolation. On the other hand the same is not always true if we apply a slightly more general construction of random Cantor sets. We also present a complete solution for the deterministic case. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008 [source]