Numerical Methods in Scientific Computing

Jos van Kan; Guus Segal; Fred Vermolen

doi:10.59490/t.2023.009

Numerical Methods in Scientific Computing

Authors

Jos van Kan

Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, The Netherlands

https://orcid.org/0009-0003-5744-5465

Guus Segal

Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, The Netherlands

Fred Vermolen

Department of Computational Mathematic, Faculty of Sciences, University of Hasselt, Belgium

https://orcid.org/0000-0003-2212-1711

DOI: https://doi.org/10.59490/t.2023.009

Keywords: Numerical mathematics

Synopsis

This is a book about numerically solving partial differential equations occurring in technical and physical contexts and the authors have set themselves a more ambitious target than to just talk about the numerics. Their aim is to show the place of numerical solutions in the general modeling process and this must inevitably lead to considerations about modeling itself. Partial differential equations usually are a consequence of applying first principles to a technical or physical problem at hand. That means, that most of the time the physics also have to be taken into account especially for validation of the numerical solution obtained. This book aims especially at engineers and scientists who have ’real world’ problems. It will concern itself less with pesky mathematical detail. For the interested reader though, we have included sections on mathematical theory to provide the necessary mathematical background. Since this treatment had to be on the superficial side we have provided further reference to the literature where necessary.

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Author Biographies

Jos van Kan, Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, The Netherlands

Jos van Kan (1944) graduated in 1968 from Delft University of Technology, Delft, Netherlands, in Numerical Analysis and was assistant professor at the Department of Mathematics of that institute until 2009. He wrote several articles on Numerical Fluid Mechanics (pressure correction methods) and has written a multigrid pressure solver for the Delft software package to solve the Navier-Stokes equations. He was teaching classes in Numerical Analysis from 1971 until 2009, and wrote several books on the subject. Currently he is a retired professor.

Guus Segal, Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, The Netherlands

Guus Segal (1948) graduated in 1971 from Delft University of Technology, Delft, Netherlands, in Numerical Analysis and was part time assistant professor at the Department of Mathematics of that institute until 2013. He also worked in the consultancy and numerical software company SEPRA in The Hague, Netherlands. He wrote a number of articles on Finite Element Methods and several articles on curvilinear Finite Volume Methods and Numerical Fluid Mechanics. He has written a book on Finite Element methods and Navier-Stokes equations. He is the main developer of the finite element package SEPRAN. He was teaching classes in Numerical Analysis from 1973 until 2013.

Fred Vermolen, Department of Computational Mathematic, Faculty of Sciences, University of Hasselt, Belgium

Fred Vermolen (1969) graduated in 1993 from Delft University of Technology, Delft, Netherlands and defended his PhD thesis on numerical methods for moving boundary problems in 1998. He has written several contributions on Stefan problems, computational mechanics, mathematical analysis and uncertainty quantification with most of the applications in medicine. He has held an assistant and associate professorship in Numerical Analysis at the Delft University from 2000 until 2020. In 2020 he started his current position as a full professor in Computational Mathematics at the University of Hasselt in Belgium.