Solution of the Helmholz equation with controllability and spectral element methods

Erkki Heikkola, Sanna Mönkkölä, Anssi Pennanen, Tuomo Rossi

Research output: Contribution to journalArticle in a proceedings journalScientificpeer-review

Abstract

We formulate the Helmholz problem as an exact conrollability problem for the time-dependent wave equation. The problem is then discretized in space domain with spectral elements leading to high accuracy and diagonal mass matrices. After discretization, exact controllability problem is reformulated as a least-squares problem, which is solved by conjugate gradient method. We illustrate the method with some numerical experiments on an acoustic scattering simulation.
Original languageEnglish
Pages (from-to)121-124
JournalJournal of Structural Mechanics
Volume38
Issue number3
Publication statusPublished - 2005
MoE publication typeA4 Article in a conference publication

Fingerprint

Spectral Element Method
Controllability
Spectral Elements
Acoustic Scattering
Exact Controllability
Least Squares Problem
Conjugate Gradient Method
Wave equation
High Accuracy
Discretization
Numerical Experiment
Simulation

Cite this

Heikkola, E., Mönkkölä, S., Pennanen, A., & Rossi, T. (2005). Solution of the Helmholz equation with controllability and spectral element methods. Journal of Structural Mechanics, 38(3), 121-124.
Heikkola, Erkki ; Mönkkölä, Sanna ; Pennanen, Anssi ; Rossi, Tuomo. / Solution of the Helmholz equation with controllability and spectral element methods. In: Journal of Structural Mechanics. 2005 ; Vol. 38, No. 3. pp. 121-124.
@article{8d9388d284ad4787b935fbef2905d69e,
title = "Solution of the Helmholz equation with controllability and spectral element methods",
abstract = "We formulate the Helmholz problem as an exact conrollability problem for the time-dependent wave equation. The problem is then discretized in space domain with spectral elements leading to high accuracy and diagonal mass matrices. After discretization, exact controllability problem is reformulated as a least-squares problem, which is solved by conjugate gradient method. We illustrate the method with some numerical experiments on an acoustic scattering simulation.",
author = "Erkki Heikkola and Sanna M{\"o}nkk{\"o}l{\"a} and Anssi Pennanen and Tuomo Rossi",
note = "Project code: C3SU00713",
year = "2005",
language = "English",
volume = "38",
pages = "121--124",
journal = "Rakenteiden Mekaniikka",
issn = "0783-6104",
number = "3",

}

Heikkola, E, Mönkkölä, S, Pennanen, A & Rossi, T 2005, 'Solution of the Helmholz equation with controllability and spectral element methods', Journal of Structural Mechanics, vol. 38, no. 3, pp. 121-124.

Solution of the Helmholz equation with controllability and spectral element methods. / Heikkola, Erkki; Mönkkölä, Sanna; Pennanen, Anssi; Rossi, Tuomo.

In: Journal of Structural Mechanics, Vol. 38, No. 3, 2005, p. 121-124.

Research output: Contribution to journalArticle in a proceedings journalScientificpeer-review

TY - JOUR

T1 - Solution of the Helmholz equation with controllability and spectral element methods

AU - Heikkola, Erkki

AU - Mönkkölä, Sanna

AU - Pennanen, Anssi

AU - Rossi, Tuomo

N1 - Project code: C3SU00713

PY - 2005

Y1 - 2005

N2 - We formulate the Helmholz problem as an exact conrollability problem for the time-dependent wave equation. The problem is then discretized in space domain with spectral elements leading to high accuracy and diagonal mass matrices. After discretization, exact controllability problem is reformulated as a least-squares problem, which is solved by conjugate gradient method. We illustrate the method with some numerical experiments on an acoustic scattering simulation.

AB - We formulate the Helmholz problem as an exact conrollability problem for the time-dependent wave equation. The problem is then discretized in space domain with spectral elements leading to high accuracy and diagonal mass matrices. After discretization, exact controllability problem is reformulated as a least-squares problem, which is solved by conjugate gradient method. We illustrate the method with some numerical experiments on an acoustic scattering simulation.

M3 - Article in a proceedings journal

VL - 38

SP - 121

EP - 124

JO - Rakenteiden Mekaniikka

JF - Rakenteiden Mekaniikka

SN - 0783-6104

IS - 3

ER -