Final report on the Copper Mountain conference on multigrid methods

The Copper Mountain Conference on Multigrid Methods was held on April 6-11, 1997. It took the same format used in the previous Copper Mountain Conferences on Multigrid Method conferences. Over 87 mathematicians from all over the world attended the meeting. 56 half-hour talks on current research topics were presented. Talks with similar content were organized into sessions. Session topics included: fluids; domain decomposition; iterative methods; basics; adaptive methods; non-linear filtering; CFD; applications; transport; algebraic solvers; supercomputing; and student paper winners

Numerical methods in phase-change problems

This paper summarizes the state of the art of the numerical solution of phase-change problems. After describing the governing equations, a review of the existing methods is presented. The emphasis is put mainly on fixed domain techniques, but a brief description of the main front-tracking methods is included. A special section is devoted to the Newton-Raphson resolution with quadratic convergence of the non-linear system of equations

ICASE

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in the areas of (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving Langley facilities and scientists; and (4) computer science

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

On the Real-Time Performance, Robustness and Accuracy of Medical Image Non-Rigid Registration

Three critical issues about medical image non-rigid registration are performance, robustness and accuracy. A registration method, which is capable of responding timely with an accurate alignment, robust against the variation of the image intensity and the missing data, is desirable for its clinical use. This work addresses all three of these issues. Unacceptable execution time of Non-rigid registration (NRR) often presents a major obstacle to its routine clinical use. We present a hybrid data partitioning method to parallelize a NRR method on a cooperative architecture, which enables us to get closer to the goal: accelerating using architecture rather than designing a parallel algorithm from scratch. to further accelerate the performance for the GPU part, a GPU optimization tool is provided to automatically optimize GPU execution configuration.;Missing data and variation of the intensity are two severe challenges for the robustness of the registration method. A novel point-based NRR method is presented to resolve mapping function (deformation field) with the point correspondence missing. The novelty of this method lies in incorporating a finite element biomechanical model into an Expectation and Maximization (EM) framework to resolve the correspondence and mapping function simultaneously. This method is extended to deal with the deformation induced by tumor resection, which imposes another challenge, i.e. incomplete intra-operative MRI. The registration is formulated as a three variable (Correspondence, Deformation Field, and Resection Region) functional minimization problem and resolved by a Nested Expectation and Maximization framework. The experimental results show the effectiveness of this method in correcting the deformation in the vicinity of the tumor. to deal with the variation of the intensity, two different methods are developed depending on the specific application. For the mono-modality registration on delayed enhanced cardiac MRI and cine MRI, a hybrid registration method is designed by unifying both intensity- and feature point-based metrics into one cost function. The experiment on the moving propagation of suspicious myocardial infarction shows effectiveness of this hybrid method. For the multi-modality registration on MRI and CT, a Mutual Information (MI)-based NRR is developed by modeling the underlying deformation as a Free-Form Deformation (FFD). MI is sensitive to the variation of the intensity due to equidistant bins. We overcome this disadvantage by designing a Top-to-Down K-means clustering method to naturally group similar intensities into one bin. The experiment shows this method can increase the accuracy of the MI-based registration.;In image registration, a finite element biomechanical model is usually employed to simulate the underlying movement of the soft tissue. We develop a multi-tissue mesh generation method to build a heterogeneous biomechanical model to realistically simulate the underlying movement of the brain. We focus on the following four critical mesh properties: tissue-dependent resolution, fidelity to tissue boundaries, smoothness of mesh surfaces, and element quality. Each mesh property can be controlled on a tissue level. The experiments on comparing the homogeneous model with the heterogeneous model demonstrate the effectiveness of the heterogeneous model in improving the registration accuracy

Studying Turbulence Using Numerical Simulation Databases

The Seventh Summer Program of the Center for Turbulence Research took place in the four-week period, July 5 to July 31, 1998. This was the largest CTR Summer Program to date, involving thirty-six participants from the U. S. and nine other countries. Thirty-one Stanford and NASA-Ames staff members facilitated and contributed to most of the Summer projects. A new feature, and perhaps a preview of the future programs, was that many of the projects were executed on non-NASA computers. These included supercomputers located in Europe as well as those operated by the Departments of Defense and Energy in the United States. In addition, several simulation programs developed by the visiting participants at their home institutions were used. Another new feature was the prevalence of lap-top personal computers which were used by several participants to carry out some of the work that in the past were performed on desk-top workstations. We expect these trends to continue as computing power is enhanced and as more researchers (many of whom CTR alumni) use numerical simulations to study turbulent flows. CTR's main role continues to be in providing a forum for the study of turbulence for engineering analysis and in facilitating intellectual exchange among the leading researchers in the field. Once again the combustion group was the largest. Turbulent combustion has enjoyed remarkable progress in using simulations to address increasingly complex and practically more relevant questions. The combustion group's studies included such challenging topics as fuel evaporation, soot chemistry, and thermonuclear reactions. The latter study was one of three projects related to the Department of Energy's ASCI Program (www.llnl.gov/asci); the other two (rocket propulsion and fire safety) were carried out in the turbulence modeling group. The flow control and acoustics group demonstrated a successful application of the so-called evolution algorithms which actually led to a previously unknown forcing strategy for jets yielding increased spreading rate. A very efficient algorithm for flow in complex geometries with moving boundaries based on the immersed boundary forcing technique was tested with very encouraging results. Also a new strategy for the destruction of aircraft trailing vortices was introduced and tested. The Reynolds Averaged Modeling (RANS) group demonstrated that the elliptic relaxation concept for RANS calculations is also applicable to transonic flows with shocks; however, prediction of laminar/turbulent transition remains an important pacing item. A large fraction of the LES effort was devoted to the development and testing of a new algorithmic procedure (as opposed to phenomenological model) for subgrid scale modeling based on regularized de-filtering of the flow variables. This appears to be a very promising approach, and a significant effort is currently underway to assess its robustness in high Reynolds number flows and in conjunction with numerical methods for complex flows. As part of the Summer Program two review tutorials were given on Turbulent structures in hydrocarbon pool fires (Sheldon Tieszen), and Turbulent combustion modeling: from RANS to LES via DNS (Luc Vervisch); and two seminars entitled Assessment of turbulence models for engineering applications (Paul Durbin) and Subgrid-scale modeling for non-premixed, turbulent reacting flows (James Riley) were presented. A number of colleagues from universities, government agencies, and industry attended the final presentations of the participants on July 31 and participated in the discussions. There are twenty-six papers in this volume grouped in five areas. Each group is preceded with an overview by its coordinator