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Symmetric System (symmetric + system)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

A discontinuous Galerkin method for elliptic interface problems with application to electroporation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2009
Grégory Guyomarc'h
Abstract We solve elliptic interface problems using a discontinuous Galerkin (DG) method, for which discontinuities in the solution and in its normal derivatives are prescribed on an interface inside the domain. Standard ways to solve interface problems with finite element methods consist in enforcing the prescribed discontinuity of the solution in the finite element space. Here, we show that the DG method provides a natural framework to enforce both discontinuities weakly in the DG formulation, provided the triangulation of the domain is fitted to the interface. The resulting discretization leads to a symmetric system that can be efficiently solved with standard algorithms. The method is shown to be optimally convergent in the L2 -norm. We apply our method to the numerical study of electroporation, a widely used medical technique with applications to gene therapy and cancer treatment. Mathematical models of electroporation involve elliptic problems with dynamic interface conditions. We discretize such problems into a sequence of elliptic interface problems that can be solved by our method. We obtain numerical results that agree with known exact solutions. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Unified approach to KdV modulations

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 10 2001
Gennady A. El
We develop a unified approach to integrating the Whitham modulation equations. Our approach is based on the formulation of the initial-value problem for the zero-dispersion KdV as the steepest descent for the scalar Riemann-Hilbert problem [6] and on the method of generating differentials for the KdV-Whitham hierarchy [9]. By assuming the hyperbolicity of the zero-dispersion limit for the KdV with general initial data, we bypass the inverse scattering transform and produce the symmetric system of algebraic equations describing motion of the modulation parameters plus the system of inequalities determining the number the oscillating phases at any fixed point on the (x, t)-plane. The resulting system effectively solves the zero-dispersion KdV with an arbitrary initial datum. © 2001 John Wiley & Sons, Inc. [source]

A segregated method for compressible flow computation Part I: isothermal compressible flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2005
Guillermo Hauke
Abstract Traditionally, coupled methods have been employed for the computation of compressible flows, whereas segregated methods have been preferred for the computation of incompressible flows. Compared to coupled methods, segregated solvers present the advantage of reduced computer memory and CPU time requirements, although at the cost of an inferior robustness. Therefore, in a series of papers we present unified computational techniques to compute compressible and incompressible flows with segregated stabilized methods. The proposed algorithms have an increased robustness compared to existing techniques, while possessing additional benefits such as employing standard pressure boundary conditions. In this first part, the thermodynamics of isothermal, thermally perfect compressible flows is set up in the framework of symmetric systems and the corresponding segregated algorithms are introduced. Copyright © 2005 John Wiley & Sons, Ltd. [source]

The Pauli potential from the differential virial theorem

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 12 2010
Á. Nagy
Abstract Recently, a first-order differential equation for the functional derivative of the kinetic energy functional is derived for spherically symmetric systems using the differential virial theorem of Nagy and March. Here, a more general first-order differential equation for the Pauli potential (valid not only for spherically symmetric systems) is derived by applying the differential virial theorem of Holas and March. The solution of the equation can be given by quantities capable of fully determining every property of a Coulomb system. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source]