Designed especially for neurobiologists, FluoRender is an interactive tool for multi-channel fluorescence microscopy data visualization and analysis.
Deep brain stimulation
BrainStimulator is a set of networks that are used in SCIRun to perform simulations of brain stimulation such as transcranial direct current stimulation (tDCS) and magnetic transcranial stimulation (TMS).
Developing software tools for science has always been a central vision of the SCI Institute.

SCI Publications

1993


C. Walshaw, M. Berzins. “Enhanced Dynamic Load Balancing of Adaptive Unstructured Meshes,” In Proc. of 1993 SIAM Conference on Parallel Processing for Scientific Computing, Vol. 2, pp. 971--978. 1993.


1992


M. Berzins, A.J. Preston, P.M. Dew, L.E. Scales. “Towards Efficient D.A.E. Solvers for the Solution of Dynamic Simulation Problems,” In Proc of I.M.A. 1989 O.D.E. Conference, Edited by I. Gladwell and J. Cash and A. Iserles, Oxford University Press, pp. 299--308. 1992.
ISBN: 0-19-853659-3



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

ABSTRACT

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.



M. Berzins, P.M. Dew, S. Hillen. “Exploiting Parallelism for Adaptive CFD Software,” In Parallelogram, pp. 14--16. February, 1992.



K.W. Brodlie, M. Berzins, P.M. Dew, A. Poon, H. Wright. “Visualization and its Use in Scientific Computation,” In Programming Environments for High-Level Scientific Problem Solving, Elsevier, pp. 293--303. 1992.



J. Lawson, M. Berzins. “Towards an Automatic Algorithm for the Numerical Solution of Parabolic P.D.E.s Using the Method of Lines,” In proc of I.M.A. 1989 O.D.E. Conference, Edited by I. Gladwell and J. Cash and A. Iserles, Oxford University Press, pp. 309--322. 1992.
ISBN: 0-19-853659-3



C. Walshaw, M. Berzins. “Dynamic Load Balancing for PDE Solvers on Adaptive Unstructured Meshes,” School of Computer Studies Research Report, No. 92.32, University of Leeds, December, 1992.



J.M. Ware, M. Berzins. “Finite Volume Techniques for Time-dependent Fluid-Flow Problems,” In Advances in Comp. Meths. for P.D.E.s VII, New Jersey, Rutgers Univ., pp. 794--798. 1992.


1991


M. Berzins, P. Baehmann, J.E. Flaherty, J. Lawson. “Towards An Automated Finite Element Solver for Time-Dependent Fluid-Flow Problems,” In MAFELAP 90, Edited by J.R. Whiteman, Academic Press, pp. 181--188. 1991.



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

ABSTRACT

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].



M. Berzins. “Balancing Space and Time Errors for Spectral Methods used with the Method of Lines for Parabolic equations,” 1991.



J. Lawson, M. Berzins, P.M. Dew. “Balancing Space and Time Errors in the Method of Lines for Parabolic Equations,” In SIAM Journal on Scientific Computing, Vol. 12, No. 3, pp. 573--594. 1991.



A.J. Preston, M. Berzins. “On Algorithms for the Location of Discontinuities for Dynamic Simulation Problems,” In Computers in Chemical Engineering, Vol. 15, No. 10, pp. 701--713. 1991.


1990


M. Berzins, A.J. Preston, P.M. Dew. “Integration Algorithms for the Dynamic Simulation of Production Processes,” In Proc of Third European Conference for Mathematics in Industry, Edited by J. Manley et al., Kluwer Academic Publishers, Stuttgart., pp. 265--271. 1990.



R.D. Skeel, M. Berzins. “A Method for the Spatial Discretisation of Parabolic Equations,” In SIAM Journal on Scientific Computing, Vol. 11, No. 1, pp. 1--32. January, 1990.


1989


M. Berzins. “Developments in NAG Library Software for Parabolic Equations,” In Scientific Software Systems, Edited by J.C. Mason and M.G. Cox, Chapman and Hall, pp. 59--72. July, 1989.
ISBN: 0412345706



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


1988


M. Berzins. “Global Error Estimation in the Method of Lines for Parabolic Equations,” In SIAM Journal on Scientific Computing, Vol. 9, pp. 687--703. 1988.



M. Berzins, R. Brankin, I. Gladwell. “Design of Stiff Integrators in the N.A.G. Library,” In Signum Bulletin, Vol. 23, No. 2, pp. 16--24. April, 1988.


1987


M. Berzins, P.M. Dew. “A Note on C0 Chebyshev Methods for Parabolic Equations,” In I.M.A. Journal of Numerical Analysis, Vol. 7, pp. 15--37. 1987.