Preconditioning Dense Complex Linear Systems from a VIM Discretization: Discretizing Maxwell*s equations using the volume integral method (VIM)

Belachew, Melisew Tefera

ISBN 10: 3846510122 / ISBN 13: 9783846510124

Published by LAP LAMBERT Academic Publishing, 2011

About this Item

Like New.

Seller Inventory # ERICA75838465101226

Bibliographic Details

• Title: Preconditioning Dense Complex Linear Systems from a VIM Discretization: Discretizing Maxwell*s equations using the volume integral method (VIM)
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2011
• Language: English
• ISBN 10: 3846510122
• ISBN 13: 9783846510124
• Binding: Paperback
• Condition: Like New
• Book Type: book

About this title

Synopsis

Angular-resolved optical scatterometry is a new promising technology for metrology in lithography for the construction of VLSI chips such as DRAMs and CPUs. In order to measure the geometry dimensions and material properties of markers and interconnect lines, one needs to solve Maxwell's equations for an electromagnetic scattering problem. The well known RCWA discretization method is too slow for 3D applications whence one takes resort to either a finite element discretization method or a volume integral method (VIM). VIM systems of equations can be solved faster than FEM systems of equations. This book focuses on an iterative solution of linear systems emanating from VIM. Each different linear system depends in a non-linear manner on several geometry, material and incoming light-wave parameters. For a typical 2D-periodic application on resist, VIM is a factor of 20 faster than RCWA. The VIM discretization leads to a dense complex linear system for the electric field for a 2D-periodic grating (3D Maxwell's equations). The coefficient matrix A is almost full but matrix-vector multiplications can be performed. Therefore; systems should be solved with an iterative solution method.

About the Author

He is a lecturer at Haramaya University. He received his B.Sc. degree in Mathematics with distinction from Dilla University. He studied his 1st M.Sc. degree in Mathematics at Norwegian University of Science and Technology (Norway) and his 2nd M.Sc. degree in Industrial and Applied Mathematics at Eindhoven University of Technology (The Netherlands).