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Showing 1 to 13 of 13 for “"interface problem"”.
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Higher Order Immersed Finite Element Methods for Interface Problems
… alongside with applications to the elliptic interface problem and the hyperbolic interface problem. In the first part, we discuss a general m-th degree IFE space for one dimensional interface problems with many polynomial-like properties, then we develop a general framework for obtaining …
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Immersed and Discontinuous Finite Element Methods
… local discontinuous Galerkin method for elliptic problems and construct optimal immersed finite element approximations and discontinuous immersed finite element methods for the Stokes interface problem. In the first part we present an error analysis for the minimal dissipation local discontinuous …
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A Class of Immersed Finite Element Spaces and Their Application to Forward and Inverse Interface Problems
… is developed for solving elliptic boundary value problems that have interfaces. IFE spaces are finite element approximation spaces which are based upon meshes that can be independent of interfaces in the domain. Three different quadratic IFE spaces and their related biquadratic IFE spaces are …
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Application of Helmholtz/Hodge Decomposition to Finite Element Methods for Two-Dimensional Maxwell's Equations
… second order scalar elliptic boundary value problems. This new approach is illustrated by a P1 finite element method. In Chapter 5, we further extend the new approach described in Chapter 4 to the interface problem for Maxwell's equations. We use the extraction formulas and multigrid method …
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Investigation of explicit finite-element time-domain methods and modeling of dispersive media and 3D high-speed circuits
… each subdomain are eliminated and a global interface problem containing only the unknowns at the via holes is obtained. The interface problem is then solved and the volume unknowns in each subdomain are recovered. This method maintains the unconditional stability of the finite element …
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Unified conformal/nonconformal domain decomposition methods for solving large-scale multi-region electromagnetic problems
… analysis of large-scale electromagnetic problems in three dimensions. These algorithms are designed to expand the capability of the FETI-DP method to accommodate more flexible interface meshes, to achieve faster convergence of the global interface problem, and to reduce numerical errors …
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Nonconforming Immersed Finite Element Methods for Interface Problems
… simulations, it usually leads to the so-called interface problems of PDEs whose coefficients are discontinuous. In this dissertation, we consider nonconforming immersed "nite element (IFE) methods and error analysis for interface problems. We "first consider the second order elliptic interface …
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Domain Decomposition Preconditioners for Hermite Collocation Problems
… from the discretization of boundary value problems. Although collocation is a very general and effective discretization technique for many PDE problems, there has been relatively little work on preconditioners for collocation problems. This thesis proposes two preconditioning methods for …
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Adiabatic thermal Child-Langmuir flow
… Because there is no known solution for the interface problem between the quantum mechanical flow of electrons inside the solid material and the classical flow of electrons in the cathode vacuum, a reinjection scheme is proposed in which the initial phase space near the cathode be maintained …
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Immersed Finite Elements for a Second Order Elliptic Operator and Their Applications
… elliptic operator and their applications to interface problems of related partial differential equations. We start with the immersed finite element methods for the second order elliptic operator with a discontinuous coefficient associated with the elliptic interface problems. We introduce an …
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Eignefunctions for Partial Differential Equations on Two-Dimensional Domains With Piecewise Constant Coefficients
… discontinuous coefficients. An example of such a problem is for modeling the diffusion of heat energy in two space dimensions, in the case where the spatial domain represents a medium consisting of two different but homogeneous materials, with periodic boundary conditions.</p> <p>Since diffusivity …
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A Hermite Cubic Immersed Finite Element Space for Beam Design Problems
… is based upon meshes that can be independent of interface of the materials used to form a beam. Both the forward and inverse problems associated with the beam equation are considered. The order of accuracy of this IFE space is numerically investigated from the point of view of both the …
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A parallel second order Cartesian method for elliptic interface problems and its application to tumor growth model
… a parallel Cartesian method to solve elliptic problems with complex interfaces and its application to elliptic irregular domain problems in the framework of a tumor growth model. This method is based on a finite differences scheme and is second order accurate in the whole domain. The …