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discontinuous coefficient
, 2010
"... Carleman estimates for the onedimensional heat equation with a ..."
On diffusion approximation with discontinuous coefficients
 Stochastic Processes and Their Applications 102
, 2002
"... Abstract. Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a diffusion process with discontinuous diffusion and ..."
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Cited by 6 (1 self)
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Abstract. Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a diffusion process with discontinuous diffusion
Operators with Discontinuous Coefficients
, 906
"... Abstract. We will show that the same type of estimates known for the fundamental solutions for scalar parabolic equations with smooth enough coefficients hold for the first order derivatives of fundamental solution with respect to space variables of scalar parabolic equations of divergence form with ..."
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with discontinuous coefficients. The estimate is very important for many applications. For example, it is important for the inverse problem identifying inclusions inside a heat conductive medium from boundary measurements. Mathematics Subject Classification(2000): 35R30. 1
transport equations with discontinuous coefficients
 Comm.PDE
, 1999
"... 1 Introduction. Linear transport equations, while interesting in their own right, also occur in the study of nonlinear transport equations such as conservation laws. In this context, one encounters discontinuous transport velocities and the question of existence and uniqueness of solutions arises. S ..."
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Cited by 20 (0 self)
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1 Introduction. Linear transport equations, while interesting in their own right, also occur in the study of nonlinear transport equations such as conservation laws. In this context, one encounters discontinuous transport velocities and the question of existence and uniqueness of solutions arises
The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
 SIAM J. Num. Anal
, 1994
"... Abstract. The authors develop finite difference methods for elliptic equations of the form V. ((x)Vu(x)) + (x)u(x) f(x) in a region in one or two space dimensions. It is assumed that gt is a simple region (e.g., a rectangle) and that a uniform rectangular grid is used. The situation is studied in wh ..."
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Cited by 266 (31 self)
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sources, as used in Peskin’s immersed boundary method. Key words, elliptic equation, finite difference methods, irregular domain, interface, discontinuous coefficients, singular source term, delta functions AMS subject classifications. 65N06, 65N50 1. Introduction. Consider
OneDimensional Transport Equations With Discontinuous Coefficients
, 1998
"... We consider onedimensional linear transport equations with bounded but possibly discontinuous coefficient a. The Cauchy problem is studied from two different points of view. In the first case we assume that a is piecewise continuous. We give an existence result and a precise description of the solu ..."
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Cited by 81 (18 self)
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We consider onedimensional linear transport equations with bounded but possibly discontinuous coefficient a. The Cauchy problem is studied from two different points of view. In the first case we assume that a is piecewise continuous. We give an existence result and a precise description
Additive Schwarz, CG and Discontinuous Coefficients
, 13
"... This paper is concerned with the performance of the conjugate gradient(CG) method with additive Schwarz preconditioner for computing unstructured finite element approximations to the elliptic problem r:aru = f; on\Omega ; u = g on @\Omega D ; @u @n = ~ g on @\Omega N : (1) Here\Omega ae IR ..."
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Cited by 8 (5 self)
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This paper is concerned with the performance of the conjugate gradient(CG) method with additive Schwarz preconditioner for computing unstructured finite element approximations to the elliptic problem r:aru = f; on\Omega ; u = g on @\Omega D ; @u @n = ~ g on @\Omega N : (1) Here\Omega ae IR 3 is a polyhedral domain with boundary @\Omega partitioned into disjoint subsets @\Omega D 6= ; and @\Omega N , each of which is composed of unions of polygons, and f , g and ~ g are suitably smooth given data. (Analogous results also hold in 2D.) We also assume that a is piecewise constant on each of d open disjoint polyhedral regions k , such that [ d k=1 k = \Omega , and we write aj k = a k where each a k 2 IR + := (0; 1) is constant. We have in mind that the regions k of different material properties are fixed but may have complicated geometry and that the overall mesh used to compute u accurately will be finer than the geometry of the k . There are many applications of this type of problem, for example in groundwater flow and in electromagnetics. After discretisation with linear finite elements on a triangulation T of \Omega\Gamma (1) reduces to the SPD system K(a)x = b(a); (2) where the stiffness matrix and load vector depend continuously on a 2 IR d + . Let h denote the diameter of T and J = max k;l fa k =a l g. It is a standard result that K(a) is illconditioned in the sense that (under suitable assumptions) (K(a)) = O(h \Gamma2 ) as h ! 0 for fixed a and (K(a)) = O(J ) as J ! 1 for fixed h. (Here denotes the 2norm condition number.) One of the striking successes of domain decomposition methods has been the construction of preconditioners for which the condition number of the preconditioned problem is bounded independently of both h and a. ...
Recovery of the Impulsive Diffusion Operator with Discontinuous Coefficient
, 2014
"... In this work impulsive diffusion operator with discontinuous coefficient is considered. Integral representation is derived and some important properties of eigenvalues are studied. Moreover, it is proven that the coefficients of the given problem are uniquely determined by the Weyl function. ..."
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In this work impulsive diffusion operator with discontinuous coefficient is considered. Integral representation is derived and some important properties of eigenvalues are studied. Moreover, it is proven that the coefficients of the given problem are uniquely determined by the Weyl function.
Additive Schwarz, CG and Discontinuous Coefficients
 the Proceedings of the Ninth International Conference on Domain Decomposition methods
, 1997
"... This paper is concerned with the performance of the conjugate gradient(CG) method with additive Schwarz preconditioner for computing unstructured finite element approximations to the elliptic problem ..."
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This paper is concerned with the performance of the conjugate gradient(CG) method with additive Schwarz preconditioner for computing unstructured finite element approximations to the elliptic problem
Maxwell’s Equations with Highly Discontinuous Coefficients
, 2006
"... In this paper we develop an OcTree discretization for Maxwell’s equations in the quasistatic regime. We then use this discretization in order to develop a multigrid method for Maxwell’s equations with highly discontinuous coefficients. We test our algorithms and compare it to other multilevel algor ..."
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In this paper we develop an OcTree discretization for Maxwell’s equations in the quasistatic regime. We then use this discretization in order to develop a multigrid method for Maxwell’s equations with highly discontinuous coefficients. We test our algorithms and compare it to other multilevel
Results 1  10
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184,384