Krylov iterative methods applied to multidimensional S[sub n] calculations in the presence of material discontinuities

We show that a Krylov iterative meihod, preconditioned with DSA, can be used to efficiently compute solutions to diffusive problems with discontinuities in material properties. We consider a lumped, linear discontinuous discretization of the S N transport equation with a 'partially consistent' DSA preconditioner. The Krylov method can be implemented in terms of the original S N source iteration coding with little modification. Results from numerical experiments show that replacing source iteration with a preconditioned Krylov method can efficiently solve problems that are virtually intractable with accelerated source iteration. Key Words: Krylov iterative methods, discrete ordinates, deterministic transport methods, diffusion synthetic acceleratio

Krylov subspace iterations for the calculation of K-Eigenvalues with sn transport codes

We apply the Implicitly Restarted Arnoldi Method (IRAM), a Krylov subspace iterative method, to the calculation of k-eigenvalues for criticality problems. We show that the method can be implemented with only modest changes to existing power iteration schemes in an SN transport code. Numerical results on three dimensional unstructured tetrahedral meshes are shown. Although we only compare the IRAM to unaccelerated power iteration, the results indicate that the IRAM is a potentially efficient and powerful technique, especially for problems with dominance ratios approaching unity. Key Words: criticality eigenvalues, Implicitly Restarted Arnoldi Method (IRAM), deterministic transport method

Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel

Fully consistent, linear discontinuous diffusion synthetic acceleration on 3D unstructured meshes

We extend a multi-level preconditioned solution method for a linear discontinuous discretization of the P{sub 1} equations in two-dimensional Cartesian geometry to three-dimensional, unstructured tetrahedral meshes. A diffusion synthetic acceleration (DSA) method based on these P{sub 1} equations is applied to linear discontinuous S{sub N} transport source iterations on tetrahedral meshes. It is a fully consistent method because the P{sub 1} equations and the transport equation are both discretized with a linear discontinuous finite element basis. Fourier analyses and computational results show the DSA scheme is stable and very effective. We compare the fully consistent scheme to other 'partially consistent' DSA methods

On the degraded effectiveness of diffusion synthetic acceleration for multidimensional sn calculations in the presence of material discontinuities

We investigate the degradation in performance of diffusion synthetic acceleration (DSA) methods in problems with discontinuities in material properties. A loss in the effectiveness of DSA schemes has been Observed before with other discretizations in two dimensions under certain conditions. We present more evidence in support of the conjecture that DSA effectiveness can degrade in multidimensional problems with discontinuities in total cross section, regardless of the particular physical configuration or spatial discretization. Through Fourier analysis and numerical experiments, we identify a set of representative problems for which established DSA schemes are ineffective, focusing on highly diffusive problems for which DSA is most needed. We consider a lumped, linear discontinuous spatial discretization of the S N transport equation on three-dimensional, unstructured tetrahedral meshes and look ata fully consistent and a 'partially consistent' DSA method for this discretization. We find that the effectiveness of both methods can be significantly degraded in the presence of material discontinuities. A Fourier analysis in the limit of decreasing cell optical thickness is shown that supports the view that the degraded effectiveness of a fully consistent DSA scheme simply reflects the failure of the spatially continuous DSA method in problems where material discontinuities are present. Key Words: diffusion synthetic acceleration, discrete ordinates, deterministic transport methods, unstructured meshe

The Role of Inhomogeneities in Supernova Shock Breakout Emission

The breakout of a supernova blast wave from its progenitor star provides strong constraints on the star and its immediate surroundings. These surroundings are shaped by mass loss from the star and can include a wide variety of inhomogeneities. Here we present results of multidimensional radiation-hydrodynamics calculations of the interactions of the supernova blast wave with inhomogeneities in the immediate surroundings of a massive Wolf-Rayet star, calculating the effect these interactions have on the shock breakout signal from supernovae.Immediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]