Geometry.Net - Math_Help_Desk: Equation Solvers

Stiffness And Nonstiff Differential Equation Solvers, II: Detecting Stiffness Wi
4 SHAMPINE, LF Stiffness and nonstiff differential equation solvers. 5 SHAMPIN~, LF Limiting precision in differential equation solvers. Math. Comput.
http://portal.acm.org/citation.cfm?id=355719.355722
Diffpack Online
A very simple Poisson equation solver in 2D (class Poisson0); explanation of Heat equation solvers as a minor extension of the Poisson equation solvers,
http://www.diffpack.com/resources/training_courses.html

Extractions: The course extends over a total of 4 days and is split in two main parts: Depending on your background you might want to skip Part I. It is possible to prepare yourself for Part II by reading Chapter 1 of the course book. The course is suitable for beginners as well as more experienced Diffpack programmers. It should be ideal if you are in the process of evaluating Diffpack. Confer the course program to see what you will learn. If the courses do not suit you, we can offer training at your own office location. With this solution we can adjust the training to your requirements and even bring your own applications into the discussion. Please contact us at training@inutech.de for details.
Chapter 4. Using Sparse Linear Equation Solvers
These solvers are optimized and parallelized for SGI platforms. Direct solvers of dense linear systems of equations are described on the INTRO_LAPACK(3s)
http://www-curri.u-strasbg.fr/documentation/calcul/doc/ProPack/3SP1/docs/doc/sgi

Extractions: Chapter 4. Using Sparse Linear Equation Solvers Prev Next Many techniques exist for solving sparse linear systems. The appropriate technique depends on many factors, including the mathematical and structural properties of matrix A , the dimension of A , and the number of right-hand sides b SGI provides two direct solvers, PSLDLT and PSLDU , and one iterative solver, DITERATIVE , for sparse linear systems of equations. These solvers are optimized and parallelized for SGI platforms. Direct solvers of dense linear systems of equations are described on the man page. This section describes some of the properties that are useful in determining a good solution technique, with some common sources of matrices with these properties. A linear system can be described as , where A is an n -by- n matrix, and x and b are n dimensional vectors. A system of this kind is considered sparse if the matrix A has a small percentage of nonzero terms (less than 10%, often less than 1%). Large sparse linear systems occur frequently in engineering and scientific applications, and the solution of these systems (finding x given A and b ) is an important and costly step.
OpenSees - Analysis Capabilities Page
Linear equation solvers, time integration schemes, and solution algorithms Linear equation solvers. The following methods provide the solution of the
http://opensees.berkeley.edu/OpenSees/analysisCapabilities.html

Extractions: Center Linear equation solvers, time integration schemes, and solution algorithms are the core of the OpenSees computational framework. The components of a solution strategy are interchangeable, allowing analysts to find sets suited to their particular problem. Outlined here are the available solution strategies. New parts of the solution strategy may be seamlessly plugged in to the existing framework. The following methods provide the solution of the linear system of equations Ku = P. Each solver is tailored to a specific matrix topology. The following methods provide the solution of the generalized eigenvalue problem Kv = MvL The numbering of the degrees of freedom in the domain is done by the following methods
Automatic Generation And Differentiation Of Partial Differential Equation Solver
of Partial Differential equation solvers with IndexFree Scripts of a numerical solver for partial differential equations using finite differences
http://www.ma.hw.ac.uk/~jitse/abstract_cs.html

Extractions: Master's thesis, Department of Computer Science, University of Twente, the Netherlands, 1999. In this thesis, a system for the automatic generation of a numerical solver for partial differential equations using finite differences is developed. Due to the high performance demands in scientific computing, the efficiency of the generated code should be comparable to hand-written code. The input consists of a high-level specification of the difference scheme. Only explicit schemes are considered. Besides generating the code for the solver, the system can also automatically differentiate the difference scheme for eg.~optimisation. This automatic differentiation should take place at the script level instead of at the source-code level to retain of the general view. The input, specifying the difference scheme, is contained in a script, which is basically a sequence of assignments. However, automatic differentiation of assignments with indexed expressions leads to the difficult problem of symbolically contracting tensors containing Kronecker deltas with non-trivial index expressions. To circumvent this problem, the script are required to be index-free. Stencil operators are provided to enable the expression of difference schemes in index-free scripts. The notion of repeating a certain action is enclosed in a special stencil operator called the iterator.
Elliptic Equation Solvers
Elliptic equation solvers. 116.6% Reply/Post ratio. outer BC for momentum constraints Hisaaki Shinkai (Fri, 5 Feb 1999); MatVecEll Paul Walker (Fri,
http://wugrav.wustl.edu/research/projects/old_cocoboard/ELLIPTIC/frameindex.html
Elliptic Equation Solvers
http://wugrav.wustl.edu/research/projects/old_cocoboard/ELLIPTIC/
SISC Volume 14 Issue 5
Using Implicit ODE Methods with Iterative Linear equation solvers in It is shown how to apply ODE solvers with iterative linear equation solvers to ODEs
http://locus.siam.org/SISC/volume-14/art_0914071.html

Extractions: Terms and Conditions of Use Abstract. The use of Chebyshev spectral methods in space on an evolution partial differential equation results, in many cases, in a stiff system of ordinary differential equations (ODEs). ODE solvers based on explicit methods will therefore be inefficient for such equations. The use of conventional implicit ODE solvers is difficult since the Jacobian matrix of the ODE system is full and large. It is shown how to apply ODE solvers with iterative linear equation solvers to ODEs coming from spectral discretizations. These ODE solvers do not use the Jacobian explicitly, but good preconditioners for the Newton matrix are needed for their efficient operation. Preconditioners of the tensor product type are developed for certain classes of hyperbolic partial differential equations (PDEs), and numerical experiments show that these preconditioners give a good performance of the ODE solver and are a substantial improvement over the performance of explicit solvers. Keywords.
SISC Volume 7 Issue 2
The Use of Iterative Linearequation solvers in Codes for Large Systems of Stiff IVP s for ODE s. Tony Chan, Kenneth Jackson. Abstract.
http://locus.siam.org/SISC/volume-07/art_0907027.html
Equation Solvers
equation solvers. equation solvers. Due to the fact that the class interface is the same for serial and parallel versions, the same source code can be
http://www.ica1.uni-stuttgart.de/publications/1999/MSH99/hlrs99/hlrs99/report/no

Extractions: Equation solvers Due to the fact that the class interface is the same for serial and parallel versions, the same source code can be used in both cases. This is demonstrated for instance in the example below where a Gauss-Seidel smoothing is performed. The method ensures consistency of the shadow values with boundary conditions and across processors. The single processor version of this subroutine does not perform communication, but uses copy operations on shadow data elements to implement boundary conditions. The operation to be performed on the data elements of the array is specified in the object GaussSeidel in the same fashion as in the Force object of Sec. . The two members and return the index values of the PE local part of the parallel array. Please note that all, if any, parallelism of the program fragment is hidden within the object and its member functions. More intelligence is built into the arrays by providing specific classes for solution schemes. In the case above, a full multigrid hierarchy is erected on top of the array holding the variables of the PDE to be solved and the Gauss-Seidel smoother is part of it. Further technical details are described in [
Scalability Analysis Of Linear Equation Solvers For Sparse Positive Definite Sys
The US Army Research Laboratory (ARL) is currently developing a suite of parallel codes to model liquid composite molding (LCM) manufacturing processes.
http://www.stormingmedia.us/14/1428/A142814.html

Extractions: Limitations: APPROVED FOR PUBLIC RELEASE Description: Final rept. Jun 2002-Aug 2003 Pages: Report Date: SEP 2003 Report number: Keywords relating to this report: COMPUTER AIDED MANUFACTURING FINITE ELEMENT ANALYSIS LINEAR ALGEBRAIC EQUATIONS PARALLEL PROCESSING ... SPARSE MATRIX Printed Format - $23.95 Adobe PDF - $8.95 Please check the box for the format you wish to order. Shipping Terms
Fast Time Domain Integral Equation Solvers For Large-Scale Electromagnetic Analy
New fast time domain integral equation (TDIE) solvers for analyzing largescale electromagnetic scattering and radiation phenomena were developed.
http://www.stormingmedia.us/61/6123/A612334.html

Extractions: Limitations: APPROVED FOR PUBLIC RELEASE Description: Final rept. 1 Mar 2001-31 Aug 2004 Pages: Report Date: OCT 2004 Report number: Keywords relating to this report: COMPUTATIONS ELECTROMAGNETIC SCATTERING INTEGRAL EQUATIONS MAXWELLS EQUATIONS ... WAVE EQUATIONS Printed Format - $23.95 Adobe PDF - $20.95 Please check the box for the format you wish to order. Shipping Terms
Comparing Krylov Linear Equation Solvers
Subject Comparing Krylov Linear equation solvers; From Charles Broyden Broyden@tesco.net ; Date Thu, 29 Jun 2000 181945 +0100
http://www.csc.fi/math_topics/Mail/NANET00-3/msg00001.html
Elmer Solver
After all equation solvers have been called, the outer iteration for the nonlinear The convergence criteria must be satisfied by all equation solvers.
http://www.csc.fi/elmer/elmersolve/fem.html

Extractions: The base FEM code of Elmer Solver is a general purpose partial differential equation (PDE) solver. Elmer Solver provides the element level discretizations of the linearized PDEs. The heat equation, Navier-Stokes equations, and the advection-reaction-diffusion equation, are solved by stabilized finite element methods. The default stabilization technique is the method of Franca, Frey and Hughes [1], in which case Elmer Solver adds locally weighted squares of the governing PDEs to the energy formulation. The user can alternatively activate the so called two-level finite element stabilization, which is an approximation of the method of residual free bubbles (RFB) [2,3]. All the material parameters can be provided to the solution routines at element nodes. The parameters can depend on place, time, or on the solution it self. For anisotropic materials, the parameters may also be given as tensors instead of scalar values. Elmer Solver provides e.g. the following FEM utilities to the programmer: Gauss integration points for different element types and desired integration accuracy Computation of the value of a function in the nodes of a given element Basis functions and their first and second derivatives with respect to global coordinate system Metric tensor of the element coordinate system, and the square root of the determinant of the Jacobian of the element's coordinate mapping
Scientific Computing FAQ: NA Software Packages On The Net
PETSc includes nonlinear and linear equation solvers that employ a variety of Newton techniques and Krylov subspace methods. In addition, PETSc provides
http://www.mathcom.com/corpdir/techinfo.mdir/scifaq/q120.html

Extractions: Mathcom Home Services Customers Tech Info ... Contact Us Packages generally include an NA library and an interpretive language for a front end. Also see Symbolic Algebra , for free symbolic algebra packages. Octave RLaB Scilab Tela ... Algae, formerly called Alki Octave is considered the closest-to-Matlab of the Matlab clones. Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically. Octave can do arithmetic for real and complex scalars and matrices, solve sets of nonlinear algebraic equations, integrate functions over finite and infinite intervals, and integrate systems of ordinary differential and differential-algebraic equations. The Octave distribution includes a 200+ page Texinfo manual. Two and three dimensional plotting is fully supported using gnuplot. The underlying numerical solvers are currently standard Fortran ones like Lapack, Linpack, Odepack, the Blas, etc., packaged in a library of C++ classes. RLab is an interactive, interpreted scientific programming environment. Rlab is a very high level language intended to provide fast prototyping and program development, as well as easy data-visualization, and processing.
Simula - An Element By Element Preconditioner For Iterative Equation Solvers
An element by element preconditioner for iterative equation solvers An element by element preconditioner for iterative equation solvers
http://www.simula.no/departments/scientific/publications/SC.8.Langtangen.1986

Extractions: @import url(http://www.simula.no/ploneColumns.css); @import url(http://www.simula.no/plone.css); @import url(http://www.simula.no/ploneCustom.css); Skip to content Search Sections Personal tools You are here: Home Departments Scientific Computing Publications An element by element preconditioner for iterative equation solvers Norwegian Network Research Seminar 2005 Oslo Extreme Programming Meetup with talk by Hans Gallis Tre nye ledere ved Simulasenteret The BESTweb research library is now accessible for the public. ... H. P. Langtangen T. Rusten A. Tveito and Document Actions Talk at the 2nd International Conference on Finite Element Methods in Water Resources, Lisboa, Portugal Note Presented by A. Tveito up one level Simula Research Laboratory
Institute For Computational Dynamics
Preconditioning of Symmetric and Non Symmetric Finite Element equation solvers. An Element by Element Preconditioner for Iterative equation solvers.
http://www.iu.hio.no/~sowille/public/confer_txt.html
Lehrstuhl Für Ingenieurinformatik Im Bauwesen - Master Thesis
Integration of linear equation solvers in the MiniFE structural analysis software integration of the Java code for the linear equation solvers into the
http://www.inf.bi.ruhr-uni-bochum.de/teaching/diploma/offers/004.xsp

Extractions: The Mini-FE software is a structural analysis program written in the Java programming language. Its core structural analysis component contains a set of state-of-the-art linear equation solvers, including numerical routine from the NAG library as native code and as highly optimized Java code. To critically evaluate the numerical equation solvers used in the Mini-FE software and to assess their relative efficiency, valid benchmark baselines need to be implemented. To this end, standard numerical solvers such as Gaussian Elimination or Jacobi's Method are to be coded in Java and integrated into the Mini-FE software. Also, a representative set of suitable structural problems are to be devised and coded using Mini-FE to provide meaningful benchmark results concerning the numerical methods used in Mini-FE.
Quantum Dynamical Systems: Numerical Codes
They range from spectral Schrodinger and Master equation solvers Schrodinger equation solvers solve for the time evolution of the wave function of a
http://t8web.lanl.gov/people/salman/icp/codes.html

Extractions: Background There are a wide variety of codes associated with this project. They range from spectral Schrodinger and Master equation solvers including conditioning and noise, to numerical treatments of self-consistent mean field theories (with and without fluctuation contributions), to nonlinear stochastic partial differential equations. Inhomogeneous mean field codes solve for the time evolution of inhomogeneous mean fields in the presence of self-consistently determined quantum fluctuations. This class of codes is under development and is designed to study the formation and evolution of nonlinear coherent structures such as domain walls and vortices in both equilibrium and nonequilibrium settings. In contrast to the homogeneous case, the mean field is now spatially dependent, which means that a partial differential equation for the mean field has to be solved, coupled in turn to the fluctuations. Thus, in practice, one has now to solve at least hundreds of thousands to millions of coupled ODEs. Codes for quantum mechanical systems solve the Schrodinger (linear and nonlinear) and Master equations (density matrix or Wigner function) in one and two dimensions. Quantum trajectory codes have been added to this code suite. Most of our codes are based on spectral split-operator methods. Applications include fundamental studies of quantum dynamics, quantum chaos, soliton transport, decoherence, cavity QED and atomic optics.
WWWTar Query
residual algorithm) linear equation solver dense.c Generic DENSE linear equation solvers band.c Generic band linear equation solvers iterativ.c
http://hpux.connect.org.uk/hppd/cgi-bin/wwwtar?/hpux/Maths/Misc/cvode-1.0/cvode-

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