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.
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.
D. Forslunk, P. Hinker, C.D. Hansen, W.St. John, S. Tenbrink, J. Brewton. High-speed Networks, Visualization and Massive Parallelism in the Advanced Computing Laboratory, In Computing Systems in Engineering, Vol. 3, No. 1-4, 1992.
C.D. Hansen, P. Hinker. Massively Parallel Isosurface Extraction, In Visualization 1992, Boston, Ma., pp. 77--83. October, 1992.
C.D. Hansen, D. Butler. Visualization '91 Workshop Report: Scientific Visualization Environments, In Computer Graphics Quarterly, Vol. 26, No. 3, pp. 213--216. August, 1992.
C.R. Johnson, R.S. MacLeod, P.R. Ershler. A Computer Model for the Study of Electrical Current Flow in the Human Thorax, In Computers in Biology and Medicine, Vol. 22, No. 5, Elsevier BV, pp. 305--323. 1992.
Electrocardiography has played an important role in the detection and characterization of heart function, both in normal and abnormal states. In this paper we present an inhomogeneous, anisotropic computer model of the human thorax for use in electrocardiography with emphasis on the calculation of transthoracic potential and current distributions. Knowledge of the current pathways in the thorax has many applications in electrocardiography and has direct utility in studies pertaining to cardiac defibrillation, forward and inverse problems, impedance tomography, and electrode placement in electrocardiography.
Keywords: scalar field methods, vector field methods, tensor field methods, cardiac heart, scientific visualization
C.R. Johnson, R.S. MacLeod, M.A. Matheson. Computer Simulations Reveal Complexity of Electrical Activity in the Human Thorax, In Computers in Physics, Vol. 6, pp. 230--237. May/June, 1992.
C.R. Johnson, R.S. MacLeod, A. Dutson. Effects of Anistropy and Inhomogeneity on Electrocardiographic Fields: A Finite Element Study, In Engineering in Medicine and Biology Society 14th Annual International Conference, IEEE Press, pp. 2009--2010. 1992.
C.R. Johnson, R.S. MacLeod. Computational Studies of Forward and Inverse Problems in Electrocardiology, 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.
C.R. Johnson, R.S. MacLeod. Nonuniform Spatial Mesh Adaption Using a Posteriori Error Estimate: Applications to Forward and Inverse Problems, In Adaptive Methods for Partial Differential Equations, Vol. 14, Edited by J.E. Flaherty and M.S. Shephard, Elsevier, pp. 311--326. 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.
R.S. MacLeod, C.R. Johnson, M.A. Matheson. Visualization Tools for Computational Electrocardiology, In Visualization in Biomedical Computing, pp. 433--444. 1992.
R.S. MacLeod, C.R. Johnson, M.A. Matheson. Visualization of cardiac bioelectricity --- a case study, In IEEE Visualization `92, pp. 411--418. 1992.
R.S. MacLeod, C.R. Johnson, M.J. Gardner B.M.. Localization of Ischemia during Coronary Angioplasty using Body Surface Potential Mapping and an Electrocardiographic Inverse Solution, In Computers in Cardiology, IEEE Press, pp. 251--254. 1992.
A. Pascucci, V. Pascucci. Uso del calcolatore nella produzione, elaborazione ed archiviazione di proiezioni parallele (Using the computer for generating, processing and archiving parallel projections), In Atti del convegno L'immagine nel rilievo, Edited by C. Cundari, Gangemi, pp. 540--561. 1992.
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.
C. Williams, J. Rasure, C.D. Hansen. The State of the Art of Visual Languages for Visualization, In Visualization 1992, Boston, Ma., pp. 202--209. October, 1992.
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.