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Mechanical quadrature methods and their splitting expansion methods of the first kind boundary integral equations on open contours
"... This paper presents mechanical quadrature methods (MQM) for solving firstkind boundary integral equations (BIE) on open contours, which possesses high accuracy O(h30) and low computing complexities, where h0 = max1md hm and hm (m = 1, ..., d) is the mesh witdth of a curved edge m of open contours . ..."
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This paper presents mechanical quadrature methods (MQM) for solving firstkind boundary integral equations (BIE) on open contours, which possesses high accuracy O(h30) and low computing complexities, where h0 = max1md hm and hm (m = 1, ..., d) is the mesh witdth of a curved edge m of open contours
Boundary integral equation for tangential derivative of flux in Laplace and Helmholtz equations
, 2006
"... In this paper, the boundary integral equations (BIEs) for the tangential derivative of flux in Laplace and Helmholtz equations are presented. These integral representations can be used in order to solve several problems in the boundary element method (BEM): cubic solutions including degrees of freed ..."
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In this paper, the boundary integral equations (BIEs) for the tangential derivative of flux in Laplace and Helmholtz equations are presented. These integral representations can be used in order to solve several problems in the boundary element method (BEM): cubic solutions including degrees
SHARP HIGHFREQUENCY ESTIMATES FOR THE HELMHOLTZ EQUATION AND APPLICATIONS TO BOUNDARY INTEGRAL EQUATIONS
"... Abstract. We consider three problems for the Helmholtz equation in interior and exterior domains in Rd, (d = 2, 3): the exterior DirichlettoNeumann and NeumanntoDirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problem ..."
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Abstract. We consider three problems for the Helmholtz equation in interior and exterior domains in Rd, (d = 2, 3): the exterior DirichlettoNeumann and NeumanntoDirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions
A parallel method for solving Laplace equations with Dirichlet data using local boundary integral equations and random walks
 SIAM J. Sci. Comput
"... ar ..."
Extrapolation and Related Techniques for Solving Elliptic Equations
 BERICHT I9135, INSTITUT FUR INFORMATIK, TU MUNCHEN
, 1992
"... Extrapolation is a wellknown numerical technique for raising the approximation order. Several variants of extrapolation can be used for elliptic partial differential equations. The basic algorithmic variants are Richardson extrapolation, truncation error extrapolation and extrapolation of the funct ..."
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Cited by 3 (2 self)
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Extrapolation is a wellknown numerical technique for raising the approximation order. Several variants of extrapolation can be used for elliptic partial differential equations. The basic algorithmic variants are Richardson extrapolation, truncation error extrapolation and extrapolation
SOLUTIONS OF THE TWODIMENSIONAL HELMHOLTZ EQUATION
, 2004
"... Physics Department. It is as close as practical to the original with some grammar xes, renumbering, and some formatting changes. ..."
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Physics Department. It is as close as practical to the original with some grammar xes, renumbering, and some formatting changes.
Effective Condition Number and Condition Number for the First Kind Boundary Integral Equations by Mechanical Quadrature Methods
"... In the previous papers [1417], we have constructed mechanical quadrature methods for solving the boundary integral equations of the …rst kind. The methods possess high accuracy O(h 3 0) and low computing complexities, where h0 = max1 m d hm and hm (m = 1;:::; d) is the mesh witdth of the correspond ..."
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In the previous papers [1417], we have constructed mechanical quadrature methods for solving the boundary integral equations of the …rst kind. The methods possess high accuracy O(h 3 0) and low computing complexities, where h0 = max1 m d hm and hm (m = 1;:::; d) is the mesh witdth
formulations of twodimensional Helmholtz
, 2014
"... discretizations for the solution of integral equation ..."
Adaptive Methods for Time Domain Boundary Integral Equations
"... This thesis is concerned with the study of transient scattering of acoustic waves by an obstacle in an infinite domain, where the scattered wave is represented in terms of time domain boundary layer potentials. The problem of finding the unknown solution of the scattering problem is thus reduced to ..."
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Cited by 1 (0 self)
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by solving a linear system. The entries of the system matrix of this linear system involve, for the case of a two dimensional scattering problem, integrals over four dimensional spacetime manifolds. An accurate computation of these integrals is crucial for the stability of this method. Using piecewise
“Iterative solutions to sequences of Helmholtz equations”
, 2012
"... The socalled Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things. Aristotle For the last 300 or so years, the exact sciences have been dominated by what is r ..."
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is really a good idea, which is the idea that one can describe the natural world using mathematical equations.
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