In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire

/pdf/templates-for-the-solution-of-linear-systems-building-blocks-28xlh68wjc.pdf

Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods

In this paper we describe the libMesh (http://libmesh.sourceforge.net) framework for parallel adaptive finite element applications. libMesh is an open-source software library that has been developed to facilitate serial and parallel simulation of multiscale, multiphysics applications using adaptive mesh refinement and coarsening strategies. The main software development is being carried out in the CFDLab (http://cfdlab.ae.utexas.edu) at the University of Texas, but as with other open-source software projects; contributions are being made elsewhere in the US and abroad. The main goals of this article are: (1) to provide a basic reference source that describes libMesh and the underlying philosophy and software design approach; (2) to give sufficient detail and references on the adaptive mesh refinement and coarsening (AMR/C) scheme for applications analysts and developers; and (3) to describe the parallel implementation and data structures with supporting discussion of domain decomposition, message passing, and details related to dynamic repartitioning for parallel AMR/C. Other aspects related to C++ programming paradigms, reusability for diverse applications, adaptive modeling, physics-independent error indicators, and similar concepts are briefly discussed. Finally, results from some applications using the library are presented and areas of future research are discussed.

libMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations

Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey

During the early 1960s, scientists began to envision problem-solving computing environments not only powerful enough to solve complex problems but also able to interact with users on human terms. While many tried to create PSEs over the next few years, by the early 1970s they had abandoned almost all of these attempts. Technology could not yet support PSEs in computational science. But the dream of the 1960s can be the reality of the 1990s: high-performance computers combined with better understanding of computing and computational science have put PSEs well within our reach. The term 'problem-solving environment' means different things to different people. A PSE is a computer system that provides all the computational facilities necessary to solve a target class of problems. These features include advanced solution methods, automatic or semi-automatic selection of solution methods, and ways to easily incorporate novel solution methods. Simple PSEs appeared early in computing without being recognized as such. Some of the capabilities of future problem-solving environments seem like science fiction, but whatever form they eventually take, their scientific and economic impact will be enormous. >

Computer as thinker/doer: problem-solving environments for computational science

Unsaturated soil mechanics has rapidly become a part of geotechnical engineering practice as a result of solutions that have emerged to a number of key problems (or challenges). The solutions have emerged from numerous research studies focusing on issues that have a hindrance to the usage of unsaturated soil mechanics. The primary challenges to the implementation of unsaturated soil mechanics can be stated as follows: (1) The need to understand the fundamental, theoretical behavior of an unsaturated soil; (2) the formulation of suitable constitutive equations and the testing for uniqueness of proposed constitutive relationships; (3) the ability to formulate and solve one or more nonlinear partial differential equations using numerical methods; (4) the determination of indirect techniques for the estimation of unsaturated soil property functions, and (5) in situ and laboratory devices for the measurement of a wide range of soil suctions. This paper explains the nature of each of the previous challenges and describes the solutions that have emerged from research studies. Computer technology has played a major role in achieving practical geotechnical engineering solutions. Computer technology has played an important role with regard to the estimation of unsaturated soil property functions and the solution of nonlinear partial differential equations. Breakthroughs in the in situ and laboratory measurement of soil suction are allowing unsaturated soil theories and formulations to be verified through use of the “observational method.” 

Unsaturated Soil Mechanics in Engineering Practice

: Topics contained in this volume include the reliability of computations; a posteriori error estimation; adaptive h-, p-, and r-refinement; method of lines and local refinement methods for time-dependent problems; parallel solution techniques; and applications of adaptive methods to problems in elasticity, fluid mechanics, and combustion. Issues of reliability, presented in the contributions by Babuska and Szabo', note the importance of specifying computational accuracy in relation to the idealizations of the mathematical model. Thus, one should envision a sequence of computations where the enhancements and refinements are added to the physical mode as the computational procedure is enriched. These ideas are a relatively new and important innovation in the field. The contributions of Berger and Hassanzadeh et al. discuss parallel adaptive procedures, which is another aspect of the field that has emerged since the early conferences and workshops. (KR)

Adaptive Methods for Partial Differential Equations

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Adaptive Methods for Partial Differential Equations