On the implementation of multigrid methods for the numerical solution of partial differential equations
department or school: Science, Faculty of
department or school: Computer Science, Department of
data provider: DSpace
degree campus: UBCV
creator: Delaney, Allen Daniel
issued: 2010-05-12T19:27:08Z
issued: 1984
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: A number of experimental implementations of the multigrid algorithm for the solution of systems of partial differential equations have been produced. One program is applicable to simple nonlinear scalar equations, the others to linear equations, scalar and systems, which may be mildly stiff. All use nested grids and residual extrapolation techniques to compute solution and error estimates very economically. One version implements list based adaptive grids to further decrease both computation and storage needed for comparable problems. Each experiment was demonstrated using a set of problems with known solutions and the program performance or nonperformance discussed. Several techniques were examined to ensure that the system of difference equations representing a given problem would be convergent. The use of artificial viscosity was found to be practical in the general case, though for linear problems the use of one-sided differencing may be superior.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/24628
note: ON THE IMPLEMENTATION OF MULTIGRTD METHODS FOR THE NUMERICAL SOLUTION OF P A R T I A L D I F F E R E N T I A L EQUATIONS By A L L E N DANIEL DELANEY B.Sc, M c G i l l University, 1964 Ph.D., M c G i l l University, 1969 A THESIS SUBMITTED I N P A R T I A L F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES The Department of Computer Science We accept t h i s t h e s i s as conforming to the required standard THE U N I V E R S I T Y OF B R I T I S H COLUMBIA November 1984 (?) A l l e n Daniel Delaney, 1984 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department o r by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . _ . . . Computer Science Department of The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date I^Un^^^ /7y/fr/ DE-6 (.3/81) Multigrid Methods ( i i ) ABSTRACT A number of experimental implementations of the multigrid algorithm for the solution of systems of p a r t i a l d i f ferent ia l equations have been pro-duced . One program is applicable to simple non-linear scalar equations, the others to l inear equations, scalar and systems, which may be mildly s t i f f . A l l use nested grids and residual extrapolation techniques to compute solution and error estimates very economically. One version implements l i s t based adaptive grids to further decrease…
has type: Thesis/Dissertation
is shown at: 10.14288/1.0051863
language: eng
degree discipline: Computer Science
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
scholar level: Graduate
type: Text
identifier URI: http://hdl.handle.net/2429/24628