61. Automatic Generation And Differentiation Of Partial Differential Equation Solver Automatic Generation and Differentiation of Partial Differential equation solvers with IndexFree Scripts. Jitse Niesen. Automatic 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.

62. Euler Message Board You must define a state vector for the system Y=(x,y,z), and a function ff(t,Y,sigma,R,b), then the differential equation solvers can be used to integrate the http://euler.sourceforge.net/board/index.php?action=view&id=156

63. Center For Computational Math Colloquium, Fall 2001 Title Fast Heatequation solvers. Abstract I give fast solvers for the heat equation based on formulas of Feynman-Kac type for the pointwise solution. http://www-math.cudenver.edu/ccm/colloq/0102/feb04.html

CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM UNIVERSITY OF COLORADO AT DENVER PLACE: Mathematics Conference Room 626 UCD Building, 1250 14th St. , Denver TIME: NOON (Refreshments served at 11:45 am) Date: Monday, February 4, 2002 Speaker: Ben Fox Affiliation: SIM-OPT Consulting, Boulder, CO. e-mail: bfox@carbon.cudenver.edu Title: Fast Heat-Equation Solvers Abstract:

64. Visualizing Magnetic Fields: Numerical Equation Solvers In Action A book (with CD) describing modeling and visualization of magnetic fields....... Name Visualizing Magnetic Fields Numerical equation solvers in Action http://www.science-search.org/index/Physics/Electromagnetism/7441.htm

Search in Science-Search.org for: What's new Top Searches Statistics Science News ... Home : Detailed Information Name: Visualizing Magnetic Fields: Numerical Equation Solvers in Action Description: A book (with CD) describing modeling and visualization of magnetic fields. Also described are the numerical algorithms used for solving Category: Electromagnetism Url: http://www.vizimag.homestead.com Date: Current Rating: Clicks/Hits Received: Rate this web site: Rating: Votes: Web site owner: Allow people to rate your site on your site Modify your link Something wrong with this resource? Report this link as broken About Us Contact Us Site Guide ... Add Science Search to Your Web Site The Science Search Directory is based on DMOZ. Science Search has modified and enhanced this data. Submitting to DMOZ: Help build the largest human-edited directory on the web. Submit a Site Open Directory Project Become an Editor Science Search's Sponsors: Goom NL

65. NERSC Math Software Libraries for many different scientific and engineering applications such as Basic Linear Algebra Subroutines (BLAS), linear algebraic equation solvers (includes a few http://hpcf.nersc.gov/software/libs/math/

High Performance Computing Facility at Lawrence Berkeley National Laboratory A DOE Office of Science User Facility Search Website help Home About Computers ... ACTS On May 26, 2004 NERSC introduced a new NERSC website at www.nersc.gov . The new site integrates the previous NERSC, HPCF and PDSF sites into one. The site contains information about the NERSC Center and its projects, NERSC News and Publications, and Information for NERSC Users. The information on the page you are now viewing is deprecated and is not being updated. Please visit the new NERSC website , in particular the HPC Users section has technical information for NERSC users. Software Software Home By Platform IBM SP PDSF HPSS Escher ... Newton Libraries Libraries Home Math Graphics I/O ... MPI Applications Applications Home Chemistry Math Visualization ... Requests Navigation column for this page: List of all available math libraries Math Libraries at NERSC The purpose of mathematical libraries is to provide users writing application codes with ready-to-use building blocks. The two major advantages that mathematical libraries offer are functionality and performance. Most of the libraries at NERSC exist primarily to offer functionality, but some, most notably the vendor supplied libraries, exist also to provide performance. Consequently, when a certain functionality is provided by more than one library (with comparable quality), the user should pick the one that has the highest performance. A rule of thumb is therefore to always look for the functionality in the IBM supplied libraries before turning to other libraries.

66. High-Performance Algorithms For Analysis And Design Solver (GPS) is a rapid matrix equation solver for largescale structural, electromagnetic and acoustic comparing GPS with other solvers for NASA benchmarks) are solicited by NASA http://solvers.larc.nasa.gov/

High-Performance Algorithms for Analysis and Design NASA's General-Purpose Solver (GPS) is a rapid matrix equation solver for large-scale structural , electromagnetic and acoustic analyses (8.3 million complex equations). GPS minimizes solution time and memory by exploiting matrix properties (sparse/dense, real/complex, symmetric), computers (sequential/parallel, from Supercomputers/Unix to PCs/Windows or Linux) and languages (FORTRAN, C++, and Java Internet Challenge (comparing GPS with other solvers for NASA benchmarks) are solicited by NASA. EIGr , a fast NASA eigensolver, calculates vibration modes and frequencies. EIGr reduced the time to calculate the first 100 vibration modes for the 5,156 equation Next Generation Space Telescope (NGST) model from 45.6 minutes to 31 seconds (88X speedup) opening the door for trade studies on more refined and accurate NGST models. To test GPS and/or EIGr, complete this form Jonathan Ransom, Branch Head g Branch Contact: Dr.Storaasli Feedback on Langley Products and Services

67. Math.com Online Solvers (equation Solving Help), Jump to Solve equations - Quadratics. Help with Online solvers, Math.com uses the QuickMath online solution engine. http://www.math.com/students/solvers/online_solvers.htm

Home Teacher Parents Glossary ... Email this page to a friend Select Tool Calculators Converters Graphers Resources Cool Tools References Study Tips Wonders of Math Search Math.com Online Solvers Fast Automatic Solutions Answers are completely explained in plain English! Click on the yellow arrow for explanations of any step. Numbers The numbers section allows you to do some popular number calculations with explanations. Jump to: Scientific Notation Percentages Algebra NEW! see every step worked out The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also ha s commands for splitting fractions into partial fractions, combining several fractions into one and canceling common factors within a fraction. Algebra Section Help Jump to: Expand Factor Simplify Cancel ... Join Fractions Graphs The plot command will generate a plot of almost any function or relation found in high school and undergraduate college mathematics. It will plot functions given in the form y = f(x), such as y = x

68. Math.com Online Solver Equations Online solvers equations. The equations section allows you to solve virtually any equation or system of equations. In most cases http://www.math.com/students/solvers/equations/equations.htm

Home Teacher Parents Glossary ... Email this page to a friend Select Tool Calculators Converters Graphers Resources Cool Tools References Study Tips Wonders of Math Search Online Solvers Equations The equations section allows you to solve virtually any equation or system of equations. In most cases, you can find exact solutions to your equations. Even when this is not possible, you may be able to get approximate solutions to almost any level of accuracy you require. It also contains a number of special commands for dealing with quadratic equations. I'm not sure what an equation is. Solve The Solve command can be uses to solve either a single equation for a single unknown from the basic solve page or to simultaneously solve a system of many equations in many unknowns from the advanced solve page . The advanced command allows you to specify whether you want approximate numerical answers as well as exact ones, and how many digits of accuracy (up to 999) you require. It also allows you to eliminate certain variables from the equations. Solve Now!

69. CS267: Notes For Lectures 15 And 16, Mar 5 And 7, 1996 Review of the Discrete Poisson equation. The Complexity of Solving the Discrete Poisson equation FISHPACK, which contains fast solvers for Poisson's equation based on a related O(N http://www.cs.berkeley.edu/~demmel/cs267/lecture24/lecture24.html

CS267: Lectures 15 and 16, Mar 5 and 7 1996 Solving the Discrete Poisson Equation using Jacobi, SOR, Conjugate Gradients, and the FFT Table of Contents Review of the Discrete Poisson Equation The Complexity of Solving the Discrete Poisson Equation Jacobi's Method Successive Overrelaxation (SOR) ... Parallelizing Higher Dimensional FFTs Review of the Discrete Poisson Equation In Lecture 13 we discussed Poisson's equation, which arises in heat flow, electrostatics, gravity, and other situations. In 2-dimensions the equation was d^2 u(x,y) d^2 u(x,y) 2D-Laplacian(u) = + = f(x,y) d x^2 d y^2 for (x,y) in a region Omega in the (x,y) plane, say the unit square < x,y < 1. To make the solution well defined, we also need to specify boundary conditions, i.e. the value of u(x,y) on the boundary of Omega. We will consider the simple case This equation describes the steady-state temperature of a uniform square plate with the boundaries held at temperature u=0, and f(x,y) equaling the external heat supplied at (x,y). In 3 dimensions, the equation is quite similar

70. Quadratic Equation Tutorials, Homework Help And Problem Solvers. Search. Mathematics, Quadratic equation Tutorials solvers Guide picks. Quadratic equation tutorials, homework help and problem solvers. http://math.about.com/cs/quadraticequation/

zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Homework Help Mathematics Math Help and Tutorials ... Algebra Quadratic Equation Home Essentials Grade By Grade Goals Math Formulas ... Math Tutors zau(256,152,145,'gob','http://z.about.com/5/ad/go.htm?gs='+gs,''); Math Help and Tutorials Math Formulas Math Lesson Plans Math Tutors ... Help zau(256,138,125,'el','http://z.about.com/0/ip/417/0.htm','');w(xb+xb); Stay Current Subscribe to the About Mathematics newsletter. Search Mathematics Quadratic Equation tutorials, homework help and problem solvers. Alphabetical Recent Up a category Complete the Squares 6 examples with step by step solutions. Complete Tutorial - Quadratic Equations Here you'll find a complete tutorial to help you understand quadratic equations. Several examples and solutions are provided. Completing the Square Complete the square to solve quadratic equations. An excellent but brief tutorial with information for when you can't factor the equation. Equations and Solutions Over 10 quadratic equations explained and resolved with simple to follow instructions. Interactive Practice Use this interactive tutorial to improve your ability to solve quadratic equations.

71. Quadratic Equation Tutorials, Homework Help And Problem Solvers. Search. Mathematics, Quadratic equation Tutorials solvers. Quadratic equation tutorials, homework help and problem solvers. Articles Resources. http://math.about.com/od/quadraticequation/

zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Homework Help Mathematics Math Help and Tutorials ... Algebra Quadratic Equation Home Essentials Grade By Grade Goals Math Formulas ... Math Tutors zau(256,152,145,'gob','http://z.about.com/5/ad/go.htm?gs='+gs,''); Math Help and Tutorials Math Formulas Math Lesson Plans Math Tutors ... Help zau(256,138,125,'el','http://z.about.com/0/ip/417/0.htm','');w(xb+xb); Stay Current Subscribe to the About Mathematics newsletter. Search Mathematics Quadratic Equation tutorials, homework help and problem solvers. Alphabetical Recent Up a category Complete the Squares 6 examples with step by step solutions. Complete Tutorial - Quadratic Equations Here you'll find a complete tutorial to help you understand quadratic equations. Several examples and solutions are provided. Completing the Square Complete the square to solve quadratic equations. An excellent but brief tutorial with information for when you can't factor the equation. Equations and Solutions Over 10 quadratic equations explained and resolved with simple to follow instructions. Interactive Practice Use this interactive tutorial to improve your ability to solve quadratic equations.

72. RECSY - High Performance Sylvester-Type Equation Solver Library it is only one part of solving the complete dense matrix equation problem Previously, this was not the case, as most of the Sylvester solvers were not based on http://www.cs.umu.se/research/parallel/recsy/

RECSY — High Performance Library for Sylvester-Type Matrix Equations Isak Jonsson and Bo Kågström Contents Introduction Sylvester-Type Matrix Equations Triangular Matrix Equations Usage ... References Introduction RECSY is a library for solving triangular Sylvester-type matrix equations. Its objectives are both speed and reliability. In order to achieve these goals, RECSY is based on novel recursive blocked algorithms , which call new high-performance kernels for solving small-sized leaf problems of the recursion tree [ Jonsson and Kågström , 2002a, 2002b]. In contrast to explicit standard blocking techniques, our recursive approach leads to an automatic variable blocking that has the potential of matching the memory hierarchies of today’s HPC systems. The RECSY library comprises a set of Fortran 90 files, which uses recursion and OpenMP for shared memory parallelism to solve eight different matrix equations, including continuous-time as well as discrete-time standard and generalized Sylvester and Lyapunov equations. Sylvester-Type Matrix Equations The Sylvester-type matrix equations considered are a set of linear matrix equations that appear and are commonly used in different control theory applications.

73. HP-18C These solvers were much more flexible than TVM solvers because they could solve any equation but they were not nearly as easy to use. http://www.hpmuseum.org/hp18c.htm

The Museum of HP Calculators HP-18C The HP-18C was a business calculator with a new folding design and a dedicated alphabetic keyboard. It was HP's first algebraic pocket calculator. (HP previously used algebraic logic on desktop calculators, portable and desktop computers, and the HP-01 calculator watch.) Besides the basic business features of time value of money, cash flows etc., it had a clock with appointments, and a very powerful equation solver. It had 4 numbered registers, plus named lists. The HP-18C was also the first calculator to be programmed by HP in the new RPL language and it is listed in the RPL family here because of this, however, this language was not made available to users of the calculator. The calculator was based on a Saturn architecture CPU. Algebraic Logic (With A Stack) The calculator used algebraic logic with parentheses (but no precedence) and the multi-line display showed what was happening at all times. (For example: 5x(2+3 would show on the display until the ) was pressed which would leave 5x5 on the display.) Though it was an algebraic machine, it had a four level "history stack" with roll up and roll down keys. The LAST key retrieved the value on the next level of the stack into the current expression.

74. Quadratic   Equation   Calculator quadratic equation calculator, quadratic calculator, algebra, algebraic equation calculator equation Calculator. Note Do not enter commas. Input MUST have the format AX2 + BX + C = 0. EXAMPLE http://www.1728.com/quadratc.htm

Quadratic   Equation   Calculator Note: Do not enter commas. Input MUST have the format: AX + BX + C = EXAMPLE: If you have the equation: then enter:       2         4      -30 click E N T E R and your answers should be 3 and -5. A= B= C= X X If you need to have the answer in fractional form then: X= This calculator works by using the Quadratic Formula: If you need to find out how to determine the quadratic formula or if you want to know about "completing the square", then click here: Deriving The Quadratic Formula Significant Figures >>> Numbers are displayed in scientific notation in the amount of significant figures you specify. For easier readibility, numbers between 1,000 and -1,000 will not be in scientific notation but will still have the same precision. You may change the number of significant figures displayed by changing the number in the box above. Most browsers, will display the answers properly but if you are seeing no answers at all, enter a zero in the box above, which will eliminate all formatting but at least you will see the answers.

75. Linear Equations Linear equation Solution. Available Since 11/18/96. View equation.java. View FloatTextField.java. http://www.alumni.caltech.edu/~chamness/equation/equation.html

Linear Equation Solution Available Since 11/18/96 View equation.java View FloatTextField.java

76. MadMax Optics - FMM Toolbox™ For MATLAB© Provides robust, fast, and highorder accurate solvers for a core set of partial differential equations - including the Laplace, Poisson and modified Helmholtz equations. free These arise throughout classical and modern physics, in areas such as electrostatics, magnetostatics, incompressible flow, astrophsyics, and computational chemistry. http://www.madmaxoptics.com/technology/products/FMMToolbox.asp

2D Toolbox Version 1.02 - Full release now available! Faster Software for Computational Physics THE FAST MULTIPOLE METHOD (FMM) A new generation of software for partial differential equations. The amount of work scales linearly with the number of unknowns and the user can control the desired precision. PRODUCT DESCRIPTION Named one of the "Top Ten Algorithms of the Century" by Computing in Science and Engineering Magazine! (Jan/Feb 2000) Our solvers are flexible, easy to use, and easy to integrate into your software. All we need is the data defining the problem - you get the solution at any set of locations you choose. No grid generation is required, saving you both time and effort. PARTICLE INTERACTIONS FMMCOUL FMMDEBYE Computes electrostatic fields at any set of target locations due to a charge and dipole distribution you provide. Obtains results in O(N) time for N sources and targets.

77. Wave Equation Solver http://galaxy.ams.sunysb.edu/frontiercalc2/PDE_Solver/wavesolver/index_wavesolve

78. ESI Home Page http://z.ca.sandia.gov/esi

Welcome to the official web site of the Equation Solver Interface (ESI) Standards Multi-lab Working Group Interface Design Effort (updated Sept-27-2001) Next Meeting: Oct 16, 2001 Livermore, CA/Albuquerque, NM Video Link View the latest C++ draft specification proposals at Terascale Go to the ESI Web Voting area. View proposals that have been voted on. Contacting us... Contact the chair Join the technical discussion, present your views, contribute ideas by publishing to the if-forum@z.ca.sandia.gov reflector. Persons interested in joining the forum are welcome to send a request to be added ( in the body of the message include "subscribe if-forum you@your.machine.edu". Visit the archives of the public forum. If we said it, it's probably in there. Visit the development note archives for even more details on the header development. Contact the webmaster for this site. Our charter... The primary goal of this effort is to develop an integral set of standards for equation-solver services and components. These standards are explicitly represented as an interoperable set of interface specifications. Motivated by the need to solve massively parallel problems, this group is especially interested in scalable solution methods, components, and tools. Sparse linear equation solver services are subject to a variety of decompositions, and we do not claim that ours is "best" in a formal sense. However, we are guided by a desire to simplify the abstractions and a need to achieve maximal performance.

79. Heat Equation Solver http://galaxy.ams.sunysb.edu/frontiercalc2/PDE_Solver/heatsolver/index_heatsolve

80. General-Purpose Equation Solver, GPS GeneralPurpose equation Solver, GPS. This fast equation solver, written by people at NASA, is available free of charge (to US citizens and residents only). http://www.engr.usask.ca/~macphed/finite/fe_resources/node297.html

Next: Math-Net Links Up: Previous: Finite Element Translators General-Purpose equation Solver, GPS This fast equation solver, written by people at NASA, is available free of charge (to US citizens and residents only). This algorithm is faster than any other used on the test cases that NASA has provided. The solver was designed to solve sparse and dense, positive definite and indefinite systems of linear equations, and to handle cases when the problem exceeds memory capacity ("out-of-core" solutions). Some information about the solver is available on the web site at http://solvers.larc.nasa.gov/ . Contact Olaf O. Storaasli for details. Roger Young and Ian MacPhedran

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