Results 1 
4 of
4
A Fast Multilevel Algorithm For Integral Equations
 SIAM J. Numer. Anal
, 1993
"... . We show how the discretization of integral equations by composite Gauss rules can be related to approximations of integral operators that converge in the operator norm, rather than strongly. From this norm convergent formulation a two level approximate inverse can be constructed whose evaluation r ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
(Show Context)
. We show how the discretization of integral equations by composite Gauss rules can be related to approximations of integral operators that converge in the operator norm, rather than strongly. From this norm convergent formulation a two level approximate inverse can be constructed whose evaluation requires no fine mesh evaluations of the integral operator. The resulting multilevel algorithm, therefore, is roughly half as costly as the AtkinsonBrakhage iteration. The algorithm is applicable to both linear and nonlinear equations. Key words. Integral equations, multilevel methods, AtkinsonBrakhage iteration, composite Gauss rule AMS(MOS) subject classifications. 45G10, 65F10, 65J15, 1. Introduction. The purpose of this paper is to show how the discretization of integral equations by composite Gauss rules can be related to approximations of integral operators that converge in the operator norm, rather than strongly. From this norm convergent formulation a two level approximate invers...
Existence And Uniqueness Of Solutions Of Nonlinear Systems Of ConductiveRadiative Heat Transfer Equations
 North Carolina State University, Center for
, 1995
"... . We prove an existence and uniqueness results for a system of nonlinear integrodifferential equations that model steadystate combined radiativeconductive heat transfer. Our approach uses two different formulations of the system as a compact fixedpoint problem. One formulation, which has been use ..."
Abstract
 Add to MetaCart
. We prove an existence and uniqueness results for a system of nonlinear integrodifferential equations that model steadystate combined radiativeconductive heat transfer. Our approach uses two different formulations of the system as a compact fixedpoint problem. One formulation, which has been used in numerical work, is used for uniqueness and a new one is used for the existence proof. Key words. radiativeconductive heat transfer, compact fixed point problems, existenceuniqueness AMS(MOS) subject classifications. 45G10, 45K05, 82A70, 1. Introduction. In [9] and [5] models for coupled radiativeconductive heat transport are discussed. These models can be expressed as nonlinear systems of transport and diffusion equations. The purpose of this paper is to prove existence and uniqueness for these systems. In the interests of simplicity, we consider only isotropic scattering, homogeneous media, and Dirichlet boundary conditions. Our approach may be extended directly to the more compli...
unknown title
"... Abstract. In this paper we describe a hybrid deterministic/Monte Carlo algorithm for neutron transport simulation. The algorithm is based on nonlinear accelerators for source iteration, using Monte Carlo methods for the purely absorbing highorder problem and a Jacobianfree Newton– Krylov iteration ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. In this paper we describe a hybrid deterministic/Monte Carlo algorithm for neutron transport simulation. The algorithm is based on nonlinear accelerators for source iteration, using Monte Carlo methods for the purely absorbing highorder problem and a Jacobianfree Newton– Krylov iteration for the loworder problem. We couple the Monte Carlo solution with the loworder problem using filtering to smooth the flux and current from the Monte Carlo solver and an analytic Jacobianvector product to avoid numerical differentiation of the Monte Carlo results. We use a continuous energy deposition tally for the Monte Carlo simulation. We conclude the paper with numerical results which illustrate the effectiveness of the new algorithm. Key words. JFNK methods, neutron transport, Monte Carlo simulation, hybrid methods
APPROVED BY:
, 2013
"... Neutron Transport Equation and kEigenvalue Problem. (Under the direction of C.T. Kelley.) The goal of this thesis is to build hybrid deterministic/Monte Carlo algorithms for solving the neutron transport equation and associated keigenvalue problem. We begin by introducing and deriving the transpor ..."
Abstract
 Add to MetaCart
(Show Context)
Neutron Transport Equation and kEigenvalue Problem. (Under the direction of C.T. Kelley.) The goal of this thesis is to build hybrid deterministic/Monte Carlo algorithms for solving the neutron transport equation and associated keigenvalue problem. We begin by introducing and deriving the transport equation before discussing a series of deterministic methods for solving the transport equation. To begin we consider momentbased acceleration techniques for both the one and twodimensional fixed source problems. Once this machinery has been developed, we will apply similar techniques for computing the dominant eigenvalue of the neutron transport equation. We’ll motivate the development of hybrid methods by describing the deficiencies of deterministic methods before describing Monte Carlo methods and their advantages. We conclude the thesis with a chapter describing the detailed implementation of hybrid methods for both the fixedsource and keigenvalue problem in both one and two space dimensions. We’ll use a series of test problems to demonstrate the effectiveness of these algorithms before hinting