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Scientific Computing

Numerical simulation of real-world phenomena provides fertile ground for building interdisciplinary relationships. The SCI Institute has a long tradition of building these relationships in a win-win fashion – a win for the theoretical and algorithmic development of numerical modeling and simulation techniques and a win for the discipline-specific science of interest. High-order and adaptive methods, uncertainty quantification, complexity analysis, and parallelization are just some of the topics being investigated by SCI faculty. These areas of computing are being applied to a wide variety of engineering applications ranging from fluid mechanics and solid mechanics to bioelectricity.


Martin Berzins

Parallel Computing

Mike Kirby

Finite Element Methods
Uncertainty Quantification

Valerio Pascucci

Scientific Data Management

Chris Johnson

Problem Solving Environments

Ross Whitaker


Chuck Hansen


Scientific Computing Project Sites:

Publications in Scientific Computing:

An Automatic Adaptive Refinement and Derefinement Method
F. Yu, C.R. Johnson. In Proceedings of the 14th IMACS World Congress, pp. 1555--1557. 1994.

High Performance Computing in Medicine: Direct and Inverse Problems in Cardiology
C.R. Johnson, R.S. MacLeod. In IEEE Engineering in Medicine and Biology Society 15th Annual International Conference, pp. 582--583. 1993.

A 3D Cellular Automata Model of the Heart
P.B. Gharpure, C.R. Johnson. In IEEE Engineering in Medicine and Biology Society 15th Annual International Conference, IEEE Press, pp. 752--753. 1993.

Computer Simulations Reveal Complexity of Electrical Activity in the Human Thorax
C.R. Johnson, R.S. MacLeod, M.A. Matheson. In Computers in Physics, Vol. 6, pp. 230--237. May/June, 1992.

An Adaptive Theta Method for the Solution of Stiff and Non-stiff Differential Equations
M. Berzins, R.M. Furzeland. In Applied Numerical Mathematics, Vol. 9, pp. 1--19. 1992.

Berzins, M. and R.M. Furzeland, An adaptive theta method for the solution of stiff and nonstiff differential
equations, Applied Numerical Mathematics 9 (1992) 1-19.

This paper describes a new adaptive method that has been developed to give improved efficiency for solving
differential equations where the degree of stiffness varies during the course df the integration or is not known
beforehand. The method is a modification of the theta method, in which the new adaptive strategy is to
automatically select the value of theta and to switch between functional iteration and Newton iteration for the
solution of the nonlinear equations arising at each integration step. The criteria for selecting theta and for
switching are established by optimising the permissible step size.

The performance of the adaptive methods is demonstrated on a range of test problems including one arising
from the method of lines solution of a convectixr-dominated partial differential equation. In some cases the new
approach halves the amount of computational work.

Effects of Anistropy and Inhomogeneity on Electrocardiographic Fields: A Finite Element Study
C.R. Johnson, R.S. MacLeod, A. Dutson. In Engineering in Medicine and Biology Society 14th Annual International Conference, IEEE Press, pp. 2009--2010. 1992.

A Computer Model for the Study of Electrical Current Flow in the Human Thorax
C.R. Johnson, R.S. MacLeod, P.R. Ershler. In Computers in Biology and Medicine, Vol. 22, No. 3, pp. 305--323. 1992.

Computational Studies of Forward and Inverse Problems in Electrocardiology
C.R. Johnson, R.S. MacLeod. In Biomedical Modeling and Simulation, Edited by J. Eisenfeld and D.S. Levine and M. Witten, Elsevier Science Publishers, Elsevier, Amsterdam pp. 283--290. 1992.

Nonuniform Spatial Mesh Adaption Using a Posteriori Error Estimate: Applications to Forward and Inverse Problems
C.R. Johnson, R.S. MacLeod. In Adaptive Methods for Partial Differential Equations, Vol. 14, Edited by J.E. Flaherty and M.S. Shephard, Elsevier, pp. 311--326. 1992.

Computer Models for Calculating Transthoracic Current Flow
C.R. Johnson, R.S. MacLeod. In IEEE Engineering in Medicine and Biology Society 13th Annual International Conference, IEEE Press, pp. 768--769. 1991.

Construction of an Inhomogeneous Model of the Human Torso for Use in Computational Electrocardiography
R.S. MacLeod, C.R. Johnson, P.R. Ershler. In IEEE Engineering in Medicine and Biology Society 13th Annual International Conference, IEEE Press, pp. 688--689. 1991.

Chebyshev Polynomial Software for Elliptic-Parabolic Systems of P.D.E.s
M. Berzins, P.M. Dew. In A.C.M. Transactions on Mathematical Software, Vol. 17, No. 2, pp. 178--206. June, 1991.

PDECHEB is a FORTRAN 77 software package that semidiscretizes a wide range of time dependent partial differential equations in one space variable. The software implements a family of spatial discretization formulas, based on piecewise Chebyshev polynomial expansions with C0 continuity. The package has been designed to be used in conjunction with a general integrator for initial value problems to provide a powerful software tool for the solution of parabolic-elliptic PDEs with coupled differential algebraic equations. Examples are provided to illustrate the use of the package with the DASSL d.a.e, integrator of Petzold [18].

Electrical Activation of the Heart: Computational Studies of the Forward and Inverse Problems in Electrocardiography
C.R. Johnson, A.E. Pollard. In Computer Assisted Analysis and Modeling, MIT Press, pp. 583--628. 1990.

Developing Software for Time-Dependent Problems Using the Method of Lines and Differential Algebraic Integrators
M. Berzins, P.M. Dew, R.M. Furzeland. In Applied Numerical Mathematics, Vol. 5, pp. 375--397. 1989.

A C1 Interpolant for Codes Based on Backward Differentiation Formulae
M. Berzins. In Applied Numerical Mathematics, Vol. 2, pp. 109--118. 1986.

This note is concerned with the provision of an interpolant for o.d.e. initial value codes based upon backward differentiation formulae (b.d.f.) in which both the solution and its first time derivative are continuous over the range of integration--a C1 interpolant. The construction and implementation of the interpolant is described and the continuity achieved in practice is illustrated by two examples.