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         Equation Solvers:     more books (100)
  1. A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence close models (NASA contractor report) by Joseph H Morrison, 1992
  2. Calculations of separated 3-D flows with a pressure-staggered Navier-Stokes equations solver (SuDoc NAS 1.26:187065) by S.-W. Kim,
  3. PolyRES, a polygon-based Richards equation solver (SuDoc Y 3.N 88:25/6366) by R. G. Hills, 1995
  4. Performance evaluation of explicit shallow-water equations solvers on the CYBER 205 (Report. Centrum voor Wiskunde en Informatica) by F. W Wubs, 1985
  5. EQUALOG: An experimental Prolog-based equation solver (Research report RC. International Business Machines Corporation. Research Division) by Peter B Sheridan, 1988
  6. High-performance equation solvers and their impact on finite element analysis (SuDoc NAS 1.15:102735) by Eugene L. Poole, 1990
  7. A study of tunable integration and control theory for the analysis of differential equation solvers (Technical report - Frank J. Seiler Research Laboratory) by Marc L Sabin, 1977
  8. Accurate elliptic differential equation solver by William F Ames, 1985
  9. Visualizing Magnetic Fields: Numerical Equation Solvers in Action (With CD-ROM) by John Stuart Beeteson, 2001
  10. Parallel-Vector Equation Solvers for Finite Element Engineering by Duc Thai Nguyen, 2001
  11. Fast Time Domain Integral Equation Solvers (IEEE Press Series on Electromagnetic Wave Theory) by Eric Michielssen, Balasubramaniam Shanker, 2010-06-08
  12. Multigrid equation solvers for large scale nonlinear finite element simulations (Report) by Mark Francis Adams, 1999
  13. A numerical equation solver in Prolog (Research report) by Michael A Covington, 1989
  14. A new order selection strategy for ordinary differential equation solvers (Technical report. Monash University. Dept. of Computer Science) by Peter Tischer, 1988

41. 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

42. 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
Overview
The course extends over a total of 4 days and is split in two main parts:
  • Part I (1 day) covers necessary preliminaries. It is intended for persons with no Diffpack experience and/or little experience with C++. It consist of modules 1-3 in the table below. Part II (3 days) consist of modules 4-14 in the table and constitutes the main part of the training.
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.
Schedule for 2005
In 2005 we have scheduled four courses in Germany. Dates, locations, and reservation deadlines are as follows:

43. 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
Chapter 4. Using Sparse Linear Equation Solvers Prev Next
Chapter 4. Using Sparse Linear Equation Solvers
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.
Sparse Matrices
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.

44. 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
Quick Links Home Download Documentation Message Board Source Code Class Interface Bugs Roadmap Search
  • Main Page About
      OpenSees
    • Capabilities ...
      Center
      OpenSees Analysis Capabilities
      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.
      Linear Equation Solvers
      The following methods provide the solution of the linear system of equations Ku = P. Each solver is tailored to a specific matrix topology.
      • Profile SPD Direct profile solver for symmetric positive definite matrices Band General Direct solver for banded unsymmetric matrices Band SPD Direct solver for banded symmetric positive definite matrices Sparse General Direct solver for unsymmetric sparse matrices Sparse Symmetric Direct solver for symmetric sparse matrices UmfPack General Direct UmfPack solver for unsymmetric matrices Full General Direct solver for unsymmetric dense matrices Conjugate Gradient Iterative solver using the preconditioned conjugate gradient method
      Eigenvalue Solvers
      The following methods provide the solution of the generalized eigenvalue problem Kv = MvL
      • Symmetric Arpack Arpack solver for symmetric matrices Band Arpack Arpack solver for banded matrices
      DOF Numberers
      The numbering of the degrees of freedom in the domain is done by the following methods

45. 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
Automatic Generation and Differentiation of Partial Differential Equation Solvers with Index-Free Scripts
Jitse Niesen. Automatic Generation and Differentiation of Partial Differential Equation Solvers with Index-Free Scripts
Master's thesis, Department of Computer Science, University of Twente, the Netherlands, 1999.
Abstract
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.

46. 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
116.6% Reply/Post ratio

47. Elliptic Equation Solvers

http://wugrav.wustl.edu/research/projects/old_cocoboard/ELLIPTIC/

48. 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
SIAM's Online Journal Archive
SEEK EXPLORE LOCATE SISC volume 14 issue 5 advanced search By using LOCUS you agree to abide by the
Terms and Conditions of Use
SISC, Volume 14 Issue 5
Using Implicit ODE Methods with Iterative Linear Equation Solvers in Spectral Methods
Ivar Lie
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.

49. 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
SIAM's Online Journal Archive
SEEK EXPLORE LOCATE SISC volume 7 issue 2 advanced search By using LOCUS you agree to abide by the
Terms and Conditions of Use
SISC, Volume 7 Issue 2
The Use of Iterative Linear-Equation Solvers in Codes for Large Systems of Stiff IVP s for ODE s
Tony Chan, Kenneth Jackson
Abstract. Keywords. iterative linear-equation solvers, inexact Newton methods, stiff-ODE solvers, initial value problems View Full Text (pdf) View References

50. 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
Next: Code Example Up: Quadrilateral arrays, regular grids Previous: Quadrilateral arrays, regular grids

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 [
Next: Code Example Up: Quadrilateral arrays, regular grids

51. 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

52. 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

53. 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
Message Prev Message Next Message Index
Comparing Krylov Linear Equation Solvers

54. 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
Finite element techniques of Elmer Solver
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

55. 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
Mathcom Home Services Customers Tech Info ... Contact Us
NA Software Packages on the Net
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
    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
    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.

    • 56. 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
    @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
    Simula
    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
    An element by element preconditioner for iterative equation solvers
    Document Actions Talk at the 2nd International Conference on Finite Element Methods in Water Resources, Lisboa, Portugal Note Presented by A. Tveito
    in this category
    up one level Simula Research Laboratory
    Visiting address:
    Martin Linges v 17, Fornebu

    57. 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
    International Scientific Conferences

    58. 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
    Hauptseite Startseite Schwarzes Brett Stellenangebote
    Forschung Publikationen Forschungsgebiete
    Lehre CIP-Pool Belegungsplan Diplomarbeiten Kursangebot
    Lehrstuhl MitarbeiterInnen
    Service Diverses Suchen Impressum
    Master Thesis Studierende Mitarbeiter Deutsch English Master Thesis Diplomarbeiten Startseite Master Thesis Proposal for cand.M.S. Naveen Kumar Chitluri ID=004
    Integration of linear equation solvers in the Mini-FE structural analysis software as benchmark baselines
    Background
    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.
    Task Assignment
    The following tasks are to be completed and documented in the masters thesis: - overview of the structure of the Mini-FE software and the interfaces for the linear equation solvers currently implemented

    59. 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
    Quantum Dynamical Systems: Numerical Codes
    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.

    60. 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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