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Kaunas University of Technology, Lithuania

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Technical University of Cluj Napoca, Romania

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The University of Texas at Arlington, United States

Mohamed El Hachemi Benbouzid
University of Brest, France

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University of Defence, Czech Republic

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University of Zilina, Slovakia

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

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

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

Zbigniew Leonowicz
Wroclaw University of Science and Technology, Poland

Miroslaw Luft
Technical University of Radom, Poland

Stanislav Marchevsky
Technical University of Kosice, Slovakia

Jerzy Mikulski
University of Economics in Katowice, Katowice, Poland

Karol Molnar
Honeywell International, Czech Republic

Thang Trung Nguyen
Ton Duc Thang University, Viet Nam

Miloslav Ohlidal
Brno University of Technology, Czech Republic

Neeta Pandey
Delhi Technological University, India

Alex Noel Joseph Raj
Shantou University, China

Marek Penhaker
VSB - Technical University of Ostrava, Czech Republic

Wasiu Oyewole Popoola
The University of Edinburgh, United Kingdom

Roman Prokop
Tomas Bata University in Zlin, Czech Republic

Karol Rastocny
University of Zilina, Slovakia

Marie Richterova
University of Defence, Czech Republic

Gheorghe Sebestyen-Pal
Technical University of Cluj Napoca, Romania

Sergey Vladimirovich Serebriannikov
National Research University "MPEI", Russian Federation

Yuriy Shmaliy
Guanajuato University, Mexico

Vladimir Schejbal
University of Pardubice, Czech Republic

Bohumil Skala
University of West Bohemia in Plzen, Czech Republic

Lorand Szabo
Technical University of Cluj Napoca, Romania

Adam Szelag
Warsaw University of Technology, Poland

Ahmadreza Tabesh
Isfahan University of Technology, Iran, Islamic Republic Of

Mauro Tropea
DIMES Department of University of Calabria, Italy

Viktor Valouch
Academy of Sciences of the Czech Republic, Czech Republic

Jiri Vodrazka
Czech Technical University in Prague, Czech Republic

Miroslav Voznak
VSB - Technical University of Ostrava, Czech Republic

He Wen
Hunan University, China

Otakar Wilfert
Brno University of Technology, Czech Republic


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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.

Keywords


Domain decomposition; fictitious domain; GMRES; Krylov method; null-space method; orthogonal projector; Schur complement.

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