Solution of the Helmholz equation with controllability and spectral element methods

Erkki Heikkola; Sanna Mönkkölä; Anssi Pennanen; Tuomo Rossi

Solution of the Helmholz equation with controllability and spectral element methods

Erkki Heikkola, Sanna Mönkkölä, Anssi Pennanen, Tuomo Rossi

VTT Technical Research Centre of Finland

Research output: Contribution to journal › Article in a proceedings journal › Scientific › peer-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 language	English
Pages (from-to)	121-124
Journal	Journal of Structural Mechanics
Volume	38
Issue number	3
Publication status	Published - 2005
MoE publication type	A4 Article in a conference publication

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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. http://rmseura.tkk.fi/rmlehti/2005/nro3/RakMek_38_3_2005.pdf

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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",

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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 -

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http://rmseura.tkk.fi/rmlehti/2005/nro3/RakMek_38_3_2005.pdf