Improving the Finite Difference Approximation in the JacobianFree Newton–Krylov Method
(2016) In Bachelor's Theses in Mathematical Sciences FMNL01 20161Mathematics (Faculty of Engineering)
 Abstract
 The Jacobianfree Newton–Krylov (JFNK) method is designed to solve a linear system of equations that appears in Newton’s method. It uses the generalized minimal residual (GMRES) method to solve the linear system and a simple function to approximate the matrixvector multiplications required in GMRES. An advantage of GMRES is the ability to check the residual of a potential solution without doing any extra computations. A previous bachelor’s thesis discovered that the residual seen by the algorithm and the actual residual differ across many test cases. This puts the validity of the solution into question and makes it difficult to implement any sort of errorchecking in the algorithm. The purpose of this thesis is to investigate the... (More)
 The Jacobianfree Newton–Krylov (JFNK) method is designed to solve a linear system of equations that appears in Newton’s method. It uses the generalized minimal residual (GMRES) method to solve the linear system and a simple function to approximate the matrixvector multiplications required in GMRES. An advantage of GMRES is the ability to check the residual of a potential solution without doing any extra computations. A previous bachelor’s thesis discovered that the residual seen by the algorithm and the actual residual differ across many test cases. This puts the validity of the solution into question and makes it difficult to implement any sort of errorchecking in the algorithm. The purpose of this thesis is to investigate the discrepancy between these residuals. Tests were run on the various problems and although they were unable to determine a concrete explanation for the behavior of the residuals, they provided valuable insight into the potential causes to investigate in the future. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/8877342
 author
 Van Heyningen, Robert ^{LU}
 supervisor

 Philipp Birken ^{LU}
 organization
 course
 FMNL01 20161
 year
 2016
 type
 M2  Bachelor Degree
 subject
 keywords
 GMRES, Jacobianfree, Fluid
 publication/series
 Bachelor's Theses in Mathematical Sciences
 report number
 LUTFNA40032016
 ISSN
 16546229
 other publication id
 2016:K9
 language
 English
 id
 8877342
 date added to LUP
 20160823 11:22:59
 date last changed
 20170501 04:09:08
@misc{8877342, abstract = {The Jacobianfree Newton–Krylov (JFNK) method is designed to solve a linear system of equations that appears in Newton’s method. It uses the generalized minimal residual (GMRES) method to solve the linear system and a simple function to approximate the matrixvector multiplications required in GMRES. An advantage of GMRES is the ability to check the residual of a potential solution without doing any extra computations. A previous bachelor’s thesis discovered that the residual seen by the algorithm and the actual residual differ across many test cases. This puts the validity of the solution into question and makes it difficult to implement any sort of errorchecking in the algorithm. The purpose of this thesis is to investigate the discrepancy between these residuals. Tests were run on the various problems and although they were unable to determine a concrete explanation for the behavior of the residuals, they provided valuable insight into the potential causes to investigate in the future.}, author = {Van Heyningen, Robert}, issn = {16546229}, keyword = {GMRES,Jacobianfree,Fluid}, language = {eng}, note = {Student Paper}, series = {Bachelor's Theses in Mathematical Sciences}, title = {Improving the Finite Difference Approximation in the JacobianFree Newton–Krylov Method}, year = {2016}, }