Projected Krylov Methods for Solving Non-Symmetric Two-by-Two Block Linear Systems Arising from Fictitious Domain Formulations

doi:10.15598/aeee.v12i2.1045

Editorial board

Darius Andriukaitis
Kaunas University of Technology, Lithuania

Alexander Argyros
The University of Sydney, Australia

Radu Arsinte
Technical University of Cluj Napoca, Romania

Ivan Baronak
Slovak University of Technology, Slovakia

Khosrow Behbehani
The University of Texas at Arlington, United States

Mohamed El Hachemi Benbouzid
University of Brest, France

Dalibor Biolek
University of Defence, Czech Republic

Klara Capova
University of Zilina, Slovakia

Erik Chromy
UPC Broadband Slovakia, Slovakia

Milan Dado
University of Zilina, Slovakia

Petr Drexler
Brno University of Technology, Czech Republic

Eva Gescheidtova
Brno University of Technology, Czech Republic

Ray-Guang Cheng
National Taiwan University of Science and Technology, Taiwan, Province of China

Gokhan Hakki Ilk
Ankara University, Turkey

Janusz Jezewski
Institute of Medical Technology and Equipment, Poland

Rene Kalus
VSB - Technical University of Ostrava, Czech Republic

Ivan Kasik
Academy of Sciences of the Czech Republic, Czech Republic

Jan Kohout
University of Defence, Czech Republic

Ondrej Krejcar
University of Hradec Kralove, Czech Republic

Miroslaw Luft
Technical University of Radom, Poland

Stanislav Marchevsky
Technical University of Kosice, Slovakia

Byung-Seo Kim
Hongik University, Korea

Valeriy Arkhin
Buryat State University, Russia

Rupak Kharel
University of Huddersfield, United Kingdom

Fayaz Hussain
Ton Duc Thang University, Vietnam

Peppino Fazio
Ca’ Foscari University of Venice, Italy

Fazel Mohammadi
University of New Haven, United States of America

Thang Trung Nguyen
Ton Duc Thang University, Vietnam

Le Anh Vu
Ton Duc Thang University, Vietnam

Miroslav Voznak
VSB - Technical University of Ostrava, Czech Republic

Zbigniew Leonowicz
Wroclaw University of Science and Technology, Poland

Wasiu Oyewole Popoola
The University of Edinburgh, United Kingdom

Yuriy S. Shmaliy
Guanajuato University, Mexico

Lorand Szabo
Technical University of Cluj Napoca, Romania

Tran Trung Duy
Posts and Telecommunications Institute of Technology, Ho Chi Minh City, Vietnam

Xingwang Li
Henan Polytechnic University, China

Huynh Van Van
Ton Duc Thang University, Vietnam

Lubos Rejfek
University of Pardubice, Czech Republic

Neeta Pandey
Delhi Technological University, India

Huynh The Thien
Ho Chi Minh City University of Technology and Education, Vietnam

Mauro Tropea
DIMES Department of University of Calabria, Italy

Gaojian Huang
Henan Polytechnic University, China

Nguyen Quang Sang
Ho Chi Minh City University of Transport, Vietnam

Anh-Tu Le
Ho Chi Minh City University of Transport, Vietnam

Phu Tran Tin
Ton Duc Thang University, Vietnam

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Projected Krylov Methods for Solving Non-Symmetric Two-by-Two Block Linear Systems Arising from Fictitious Domain Formulations

Radek Kucera, Tomas Kozubek, Alexandros Markopoulos, Jaroslav Haslinger, Lukas Mocek

DOI: 10.15598/aeee.v12i2.1045

Abstract

The paper deals with the solution of large non-symmetric two-by-two block linear systems with a singular leading submatrix. Our algorithm consists of two levels. The outer level combines the Schur complement reduction with the orthogonal projectors that leads to the linear equation on subspaces. To solve this equation, we use a Krylov-type method representing the inner level of the algorithm. We propose a general technique how to get from the standard Krylov methods their projected variants generating iterations on subspaces. Then we derive the projected GMRES. The efficiency of our approach is illustrated by examples arising from the combination of the fictitious domain and FETI method.