Computing and Visualization in Science Regular article The NUMLAB numerical laboratory for computation and visualisation

A large range of software environments addresses numerical simulation, interactive visualisation and computational steering. Most such environments are designed to cover a limited application domain, such as finite element or finite difference packages, symbolic or linear algebra computations or image processing. Their software structure rarely provides a simple and extensible mathematical model for the underlying mathematics. Thus, assembling numerical simulations from computational and visualisation blocks, as well as building such blocks is a difficult task for the researcher in numerical simulation.This paper presents the NumLab environment, a single numerical laboratory for computational and visualisation applications. Its software architecture one-to-one models fundamental numerical mathematical concepts and presents a generic framework for a large class of computational applications. Partial and ordinary differential equations, transient boundary value problems, linear and non-linear systems, matrix computations, image and signal processing, and other applications all use the same software architecture and are built in a simple and interactive visual manner. NumLab’s one-to-one modelled mathematical concepts are illustrated with various applications.

[1]  Cristian Sminchisescu,et al.  Combining object orientation and dataflow modelling in the VISSION simulation system , 1999, Proceedings Technology of Object-Oriented Languages and Systems. TOOLS 29 (Cat. No.PR00275).

[2]  Donald P. Greenberg,et al.  A progressive refinement approach to fast radiosity image generation , 1988, SIGGRAPH.

[3]  Owe Axelsson,et al.  The Finite Element Method , 1984 .

[4]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[5]  J. M. Watt.  Numerical Initial Value Problems in Ordinary Differential Equations , 1972 .

[6]  William Schroeder,et al.  The Visualization Toolkit: An Object-Oriented Approach to 3-D Graphics , 1997 .

[7]  V. A. Barker,et al.  Finite element solution of boundary value problems , 1984 .

[8]  R. Dembo,et al.  INEXACT NEWTON METHODS , 1982 .

[9]  James Martin,et al.  Object-oriented analysis and design , 1992 .

[10]  J. Maubach,et al.  Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems , 1997 .

[11]  Lloyd Treinish,et al.  An extended data-flow architecture for data analysis and visualization , 1995, COMG.

[12]  S. Margenov,et al.  Optimal algebraic multilevel preconditioning for local refinement along a line , 1995, Numer. Linear Algebra Appl..

[13]  William Layton,et al.  A posteriori error estimators for a two-level finite element method for the Navier-Stokes equations , 1996 .

[14]  Ulrich Pinkall,et al.  Oorange: A Virtual Laboratory for Experimental Mathematics , 1995, VisMath.

[15]  J. Butcher.  The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods , 1987 .

[16]  M. Fortin,et al.  A stable finite element for the stokes equations , 1984 .

[17]  Jean-Marc Nerson,et al.  Object-Oriented Analysis and Design , 1992, TOOLS.

[18]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[19]  Gabriel Wittum,et al.  Multigrid Methods V , 1998 .

[20]  Timothy A. Budd,et al.  An introduction to object-oriented programming , 1991 .

[21]  簡聰富,et al.  物件導向軟體之架構(Object-Oriented Software Construction)探討 , 1989 .

[22]  Christopher R. Johnson,et al.  The SCIRun Computational Steering Software System , 1997, SciTools.

[23]  William Ribarsky,et al.  Object-oriented, dataflow visualization system-a paradigm shift? , 1992, Proceedings Visualization '92.

[24]  M. Todd.  The Computation of Fixed Points and Applications , 1976 .

[25]  M. N. Vrahatis,et al.  Ordinary Differential Equations In Theory and Practice , 1997, IEEE Computational Science and Engineering.

[26]  Alexandru Telea,et al.  VISSION: An Object Oriented Dataflow System for Simulation and Visualization , 1999, VisSym.

[27]  O. Axelsson.  A generalized conjugate gradient, least square method , 1987 .

[28]  Lutz Tobiska,et al.  Numerical Methods for Singularly Perturbed Differential Equations , 1996 .

[29]  Josie Wernecke,et al.  The inventor mentor - programming object-oriented 3D graphics with Open Inventor, release 2 , 1993 .

[30]  曹志浩,et al.  ON ALGEBRAIC MULTILEVEL PRECONDITIONING METHODS , 1993 .

[31]  P. Vassilevski,et al.  Algebraic multilevel preconditioning methods. I , 1989 .

[33]  Arjeh M. Cohen,et al.  On the Role of OpenMath in Interactive Mathematical Documents , 2001, J. Symb. Comput..

[34]  Joseph M. Maubach,et al.  Local bisection refinement for $n$-simplicial grids generated by reflection , 2017 .

[35]  Gabriel Wittum,et al.  Adaptive Methods — Algorithms, Theory and Applications , 1994 .

[36]  A. Bruaset,et al.  A Comprehensive Set of Tools for Solving Partial Differential Equations; Diffpack , 1997 .

[37]  James E. Rumbaugh,et al.  Object-Oriented Modelling and Design , 1991 .

[38]  David H. Laidlaw,et al.  The application visualization system: a computational environment for scientific visualization , 1989, IEEE Computer Graphics and Applications.

[39]  Homer F. Walker,et al.  Globally Convergent Inexact Newton Methods , 1994, SIAM J. Optim..

[40]  William Layton,et al.  Robust methods for highly nonsymmetric problems , 1994 .

[41]  Michael F. Cohen,et al.  Radiosity and realistic image synthesis , 1993 .

[42]  P. Raviart,et al.  Conforming and nonconforming finite element methods for solving the stationary Stokes equations I , 1973 .