SCI Publications
2000
M. Berzins.
“An Introduction to Mesh Quality,” In Lectures notes for 31st Lecture Series on Computational Fluid Mechanics, Rhode st Genessee, Brussels, Belgium, Edited by N.P. Weatherill and H. Deconink, Von Karman Institute for Fluid Mechanics, pp. 21 pages. March, 2000.
ISSN: 0377-8312
M. Berzins.
“Solution-Based Mesh Quality Indicators for Triangular and Tetrahedral Meshes,” In International Journal of Computational Geometry and Applications, Vol. 10, No. 3, pp. 333-346. June, 2000.
M. Berzins.
“A New Metric for Dynamic Load Balancing,” In Applied Mathematical Modelling, Vol. 25, Note: Special issue on dynamic load balancing, pp. 141--151. 2000.
M. Berzins.
“A Data-Bounded Quadratic Interpolant on Triangles and Tetrahedra,” In SIAM Journal on Scientific Computing, Vol. 22, No. 1, pp. 177--197. 2000.
S. Ghorai, A.S. Tomlin, M. Berzins.
“Resolution of pollutant concentrations in the boundary layer using a fully 3-D adaptive gridding technique,” In Atmospheric Environment, Vol. 34, No. 18, pp. 2851-2863. 2000.
C.E. Goodyer, R. Fairlie, M. Berzins, L.E. Scales.
“An In-depth Investigation of the Multigrid Approach to Steady and Transient EHL Problems,” In Thinning Films and Tribological InterfacesProceedings of the 26th Leeds-Lyon Symposium on Tribology, Tribology Series, Vol. 38, Edited by D. Dowson, M. Priest, C.M. Taylor, P. Ehret, T.H.C. Childs, G. Dalmaz, A.A. Lubrecht, Y. Berthier, L. Flamand and J.-M. Georges, Elsevier, pp. 95--102. 2000.
ISSN: 0167-8922
Multigrid methods have proved robust and highly desirable in terms of the iteration speed in solving elastohydrodynamic lubrication (EHL) problems. Lubrecht, Venner and Ehret, amongst others, have shown that multigrid can be successfully used to obtain converged solutions for steady problems. steady problems.
A detailed study reinforces these results but also shows, in some cases, that while multigrid techniques give initial rapid convergence, the residuals - having dropped to a low level - may reach a stalling point, mainly due to the cavitation region. The study will explain this behaviour in terms of the iterative scheme and show how, if this happens, the errors in the fine grid solution can be reduced further. Example results of both steady and transient EHL problems (including a thermal viscoelastic case) are shown with further developments into adaptive meshes considered.
A.S. Tomlin, S. Ghorai, G. Hart, M. Berzins.
“3-D Adaptive Unstructured Meshes in Air Pollution Modelling,” In Environmental Modeling and Software, Vol. 15, No. 4, pp. 681--692. 2000.
N. Touheed, P. Selwood, P.K. Jimack, M. Berzins.
“A Comparison of Some Dynamic Load Balancing Algorithms for a Parallel Adaptive Flow Solver,” In Parallel Computing, Vol. 26, No. 12, pp. 1535--1554. 2000.
1999
M. Berzins, L.J.K. Durbeck.
“Unstructured Mesh Methods Applied to Hyperbolic PDEs with Source Terms: Error Estimates and Mesh Quality,” In Godunov Methods: Theory and Applications Conference and Short Course, Oxford. numeritek Ltd.URL, October, 1999.
M. Berzins, J. Nash, P. Selwood.
“Parallel Solution of Reacting Flow Problems using Unstructured Tetrahedral Meshes,” In Proceedings of 9th SIAM Parallel Processing for Scientific Computing, Philadelphia, PA, 1999.
ISBN: 0-89871-435-4
M. Berzins.
“A Solution Based H1 Norm Triangular Mesh Quality Indicator,” In Grid Generation and Adaptive Algorithms, Edited by Marshal W. Bern, Joseph E. Flaherty, Mitchell Luskin, Springer, pp. 77-88. 1999.
The issue of mesh quality measures for triangular (and tetrahedral) meshes is considered. A new mesh quality measure is based both on geometrical and solution information and is derived by considering the error in the H 1 norm when linear triangular elements are used to approximate a quadratic function. The new measure is then compared with the recent mesh quality measure based on the L 2 norm. Simple examples are used to show that the choice of norm is critical in deciding what is a good triangulation
M. Berzins.
“Mesh Quality - Geometry, Error Estimates or Both?,” In Engineering and Computers, Vol. 15, pp. 236--247. 1999.
T.H.C. Childs, M. Berzins, G.R. Ryder, A. Towtoni.
“Selective Laser Sintering of an Amorphous Polymer-Simulations and Experiments,” In Proceedings of the Institution of Mechanical Engineers Part B: Journal of Engineering Manufacture, Vol. 213, No. B4, pp. 333--349. 1999.
J. Nash, P. Dew, M. Berzins.
“Using SADTs to Support Irregular Computational Problems,” In International Symposium on Parallel Architectures, Algorithms, and Networks, IEEE Computer Society, Los Alamitos, CA, USA pp. 338--344. 1999.
ISSN: 1087-4089
DOI: 10.1109/ISPAN.1999.778961
J. Nash, M. Berzins, P. Selwood.
“A Structured SADT Approach to the Support of a Parallel Adaptive 3D CFD Code,” In Euro-Par'99 Parallel Processing, Springer Nature, pp. 651--658. 1999.
DOI: 10.1007/3-540-48311-x_91
E.M. Nurgat, M. Berzins, L.E. Scales.
“Solving EHL Problems Using Iterative Multigrid and Homotopy Methods,” In ASME Journal of Tribology, Vol. 121, pp. 28--34. January, 1999.
P. Selwood, M. Berzins.
“Portable Parallel Adaptation of Unstructured Tetrahedral Meshes,” In Concurrency, Vol. 11, No. 13, pp. 1--22. 1999.
A. Tomlin, S. Ghorai, G. Hart, M. Berzins.
“3D adaptive unstructured meshes for air pollution modelling,” In Environmental Management and Health, Vol. 10, No. 4, pp. 267-275. 1999.
DOI: 10.1108/09566169910276238
M. Walkley, M. Berzins.
“A finite element model for the one-dimensional extended Boussinesq equations,” In International Journal for Numerical Methods in Fluids, Vol. 29, pp. 143--157. 1999.
1998
M. Berzins, P.J. Capon, P.K. Jimack.
“On Spatial Adaptivity and Interpolation When Using the Method of Lines,” In Applied Numerical Mathematics, Vol. 26, pp. 117--134. 1998.