M. Holst, Multilevel Methods for the Poisson-Boltzmann Equation, PhD thesis, Numerical Computing Group, University of Illinois at Urbana-Champaign, 1993. Also published as Tech. Rep. UIUCDCS-R03 -1821.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....approach developed in [4] and [5] to scalar second order elliptic boundary value problems in two dimensions with discontinuous coefficients. Such problems arise in various application areas, including flow in heterogeneous porous media (see e.g. 11] neutron transport [1] and biophysics [7]. In many physical applications, one is interested not only in an accurate approximation of the physical quantity that satisfies the scalar equation, but also in certain of its derivatives. For example, fluid flow in a porous medium can be modelled by the equation Gamma r Delta (arp) f (1) ....

M. J. Holst. Multilevel Methods for the Poisson-Boltzmann Equation. PhD thesis, University of Illinois at Urbana-Champaign, 1993.

....approach developed in [4] and [5] to scalar second order elliptic boundary value problems in two dimensions with discontinuous coefficients. Such problems arise in various application areas, including flow in heterogeneous porous media (see e.g. 12] neutron transport [1] and biophysics [7]. In many physical applications, one is interested not only in an accurate approximation of the physical quantity that satisfies the scalar equation, but also in certain of its derivatives. For example, fluid flow in a porous medium can be modelled by the equation Gamma r Delta (arp) f (1) ....

M. J. Holst. Multilevel Methods for the Poisson-Boltzmann Equation. PhD thesis, University of Illinois at Urbana-Champaign, 1993.

....approach developed in [4] and [5] to scalar second order elliptic boundary value problems in two dimensions with discontinuous coefficients. Such problems arise in various application areas, including flow in heterogeneous porous media (see, e.g. 12] neutron transport [1] and biophysics [7]. In many physical applications, one is interested not only in an accurate approximation of the physical quantity that satisfies the scalar equation, but also in certain of its derivatives. For example, fluid flow in a porous medium can be modelled by the equation Gammar Delta (arp) f (1) for ....

M. J. Holst. Multilevel Methods for the Poisson-Boltzmann Equation. Ph.D. thesis, University of Illinois at Urbana-Champaign, 1993.

....very slowly. Special techniques are needed to handled some of the problems. In this paper, we consider PDEs whose coefficients have jumps of several orders of magnitude. Such problems arise in various applications such as flow in heterogeneous porous media [2] neutron transport [1] biophysics [18], etc. The finite element difference discretization has to be handled carefully [3, 20, 27] Despite this, suppose the discretization is properly done. We want to derive a multigrid method which is as insensitive to the jumps as possible. A typical approach of improving the convergence is to ....

M. J. Holst. Multilevel Methods for the Poisson-Boltzmann Equation. PhD thesis, University of Illinois, Urbana-Champaign, 1993.

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M. Holst, Multilevel Methods for the Poisson-Boltzmann Equation, PhD thesis, Numerical Computing Group, University of Illinois at Urbana-Champaign, 1993. Also published as Tech. Rep. UIUCDCS-R03 -1821.

No context found.

M. Holst, Multilevel methods for the Poisson-Boltzmann equation, Ph.D. thesis, Numerical Computing Group, Department of Computer Science, University of Illinois at UrbanaChampaign, 1993, Also published as Tech. Rep. UIUCDCS-R-03-1821.

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M. Holst, Multilevel methods for the Poisson-Boltzmann equation, Ph.D. thesis, Numerical Computing Group, Department of Computer Science, University of Illinois at Urbana-Champaign, 1993.

....existing methods. 2. Discretizing the PBE The infinite domain of equation (1. 1) is often truncated to a finite domain Omega ae R 3 with boundary Gamma, and boundary conditions on Gamma are provided by a known analytical solution; detailed discussions appear in Tanford [46] and in references [29, 28]. The equation then becomes: Gamma r Delta (fflru) sinh(u) f in Omega ae R 3 ; u = g on Gamma; 2.1) where the source term in equation (1.1) has been denoted as the generic function f . The functions ffl and may be only piecewise continuous functions on Omega Gamma although we ....

....in the case of tensor product meshes allows for very efficient implementations of iterative methods for numerical solution of the discrete linear and nonlinear equations; the seven banded form is depicted in Figure 2.3 for a 3 Theta 3 Theta 3 tensor product mesh. It is not difficult to show [29, 28] that the matrix A in (2.2) is symmetric positive definite (SPD) Much more difficult questions are the well posedness of the full nonlinear system (2.2) as well as the original problem (2.1) however, it can be shown that both (2.2) and (2.1) have unique solutions depending continuously on the ....

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M. Holst, Multilevel methods for the Poisson-Boltzmann equation, Ph.D. thesis, Numerical Computing Group, Department of Computer Science, University of Illinois at Urbana-Champaign, 1993.

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