Modal Quantities and Their Usage for Evaluation of Radiated Sound Power

Total Page:16

File Type:pdf, Size:1020Kb

Modal Quantities and Their Usage for Evaluation of Radiated Sound Power Fakultät für Maschinenwesen Modal Quantities and Their Usage for Evaluation of Radiated Sound Power Lennart Dennis Moheit Vollständiger Abdruck der von der Fakultät für Maschinenwesen der Technischen Universität München zur Erlangung des akademischen Grades eines Doktor-Ingenieurs (Dr.-Ing.) genehmigten Dissertation. Vorsitzender: Prof. Dr. Carlo L. Bottasso Prüfer der Dissertation: 1. Prof. Dr.-Ing. Steffen Marburg 2. Prof. Dr. Andrés Prieto Die Dissertation wurde am 25.05.2020 bei der Technischen Universität München eingereicht und durch die Fakultät für Maschinenwesen am 01.11.2020 angenommen. a) b) Figure 1: Prof. Richard Feynman lecturing on modes to undergraduates in 1962 (a) and his summary on the topic on the blackboard (b) [1]. III Abstract Exterior problems describe effects in not entirely closed areas. They are an essential field of acoustics in which, for example, unwanted environmental noise from technical equipment needs to be minimized or the exterior noise of vehicles is optimized. In addition, the radiated sound power outdoors is usually used to describe sound sources. Since experimental investigations are often expensive and associated with uncertainties, the use of numerical methods is becoming increasingly important. Despite considerable technical and methodological developments in recent years, the calculation of exterior acoustic problems is still very expensive in terms of time and memory requirements and there is a substantial need to develop efficient methods and algorithms for these problems. Modal superposition is a well-established and efficient mathematical concept applied in structural dynamics and interior acoustics. However, the transfer to exterior acoustics is complex due to the specific mathematical properties of the systems resulting from the boundary conditions. With the frequency-dependent acoustic radiation modes (ARM) and the frequency-independent normal modes (NM), two modal quantities have been documented in the literature that potentially provide a benefit in efficiency compared to conventionally used harmonic analysis. While ARM based on the boundary element method (BEM) are already widely investigated and used in practice, NM based on the finite and infinite element method (FEM, IFEM) are relatively new and the relationship to ARM is not well understood. The present dissertation addresses these knowledge gaps and contributes to a deeper understanding of modal quantities in exterior acoustics. Tools and criteria are developed to determine physically relevant modes for the efficient numerical solution of these problems. For the first time, ARM are determined based on the frequency-independent system matrices of FEM and IFEM in order to create the same calculation basis for both modal methods. Their properties and dependencies on the underlying numerical approaches are analyzed in depth and experiences are made for a good balance between efficiency and accuracy. Appropriate models are used to investigate the nature and acoustic significance of the modes, thus developing a deeper understanding of their physical effects. It is described how the modes belong to different groups and criteria and methods for the identification and classification of the different types and their acoustic effects are developed on the basis of mathematical properties of the corresponding eigenvalues and eigenvectors. Based on the proposed and tested tools, this work presents essential innovations and findings on ARM and NM for the efficient solution of exterior acoustic problems. For the primarily investigated NM and simple radiator geometries with cavities it is shown that, with a considerably reduced modal basis, a very high accuracy (relative error of the sound power compared to harmonic analysis below 1%) can be achieved in wide frequency ranges. IV Kurzfassung Außenraumprobleme beschreiben Effekte in nicht vollständig geschlossenen Gebieten. Sie sind ein wesentliches Aufgabengebiet der Akustik, in dem beispielsweise unerwünschter Umgebungslärm techni- scher Anlagen minimiert oder die Außengeräusche von Fahrzeugen optimiert werden sollen. Darüber hinaus wird zur Beschreibung von Schallquellen in der Regel die abgestrahlte Schallleistung im Freien herangezogen. Dementsprechend aufwändig und unsicherheitsbehaftet gestalten sich häufig messtech- nische Untersuchungen, sodass die Verwendung numerischer Verfahren vermehrt in den Fokus rückt. Die Berechnung akustischer Außenraumprobleme ist trotz erheblicher technischer und methodischer Entwicklungen in den vergangenen Jahren noch immer sehr zeit- und ressourcenintensiv und es besteht ein hoher Bedarf zur Entwicklung effizienter Methoden und Algorithmen für diese Probleme. Modale Superposition ist ein in strukturdynamischen und Innenraum-akustischen Problemstellungen etabliertes und effizientes numerisches Lösungsverfahren. Allerdings gestaltet sich deren Übertragung auf den akustischen Außenraum aufgrund der spezifischen mathematischen Eigenschaften der Syste- me infolge der Randbedingungen aufwändig. Mit den frequenzabhängigen acoustic radiation modes (ARM) und den frequenzunabhängigen normal modes (NM) sind in der Literatur zwei modale Größen dokumentiert, die gegenüber der klassischerweise verwendeten harmonischen Analyse potentiell einen Effizienzvorteil liefern können. Während die ARM auf der Basis der Randelementemethode (BEM) bereits vielfältig untersucht und praktisch eingesetzt werden, sind NM auf der Grundlage von Finite und Infinite Elemente Methode (FEM, IFEM) sowie die Zusammenhänge zu den ARM wenig erforscht. Die vorliegende Dissertation befasst sich mit diesen Wissenslücken und trägt zu einem tieferen Verständ- nis modaler Größen in akustischen Außenraumproblemen bei. Zur Ermittlung physikalisch relevanter Moden für die effiziente numerische Lösung der Außenraumakustik werden Werkzeuge und Kriterien entwickelt. Hierfür werden erstmals ARM auf Grundlage der frequenzunabhängigen Systemmatrizen von FEM und IFEM bestimmt, um für die beiden modalen Verfahren die gleiche Berechnungsbasis zu schaffen. Es werden die Eigenschaften und Abhängigkeiten der modalen Verfahren von den zu- grundeliegenden numerischen Methoden tiefergehend analysiert und Erfahrungswerte für eine gute Balance zwischen Rechenaufwand und Genauigkeit generiert. Anhand geeigneter Modelle werden die Beschaffenheit und die akustische Bedeutung der Moden untersucht und so ein tiefergehendes Verständnis ihrer physikalischen Effekte entwickelt. Es werden Gruppenzugehörigkeiten beschrieben und Kriterien und Verfahren zur Identifikation und Klassifizierung unterschiedlich gearteter und wirkender Moden anhand mathematischer Eigenschaften der Eigenwerte und -vektoren entwickelt. Zur effizienten Lösung akustischer Außenraumprobleme stellt diese Arbeit mit den vorgeschlagenen und erprobten Werkzeugen wesentliche Neuerungen und Erkenntnisse zu ARM und NM vor. Für die schwerpunktmäßig untersuchten NM und einfache Strahlergeometrien mit Kavität wird gezeigt, dass mit einer stark reduzierten modalen Basis in weiten Frequenzbereichen eine sehr hohe Genauigkeit (relativer Fehler der Schallleistung gegenüber harmonischer Analyse unter 1%) erzielt werden kann. V Preface / Vorwort Während dieser scheinbar niemals enden wollenden Arbeit haben mich viele wunderbare Menschen unterstützt, denen ich von Herzen danken möchte. Mein allergrößtes und allerherzlichstes Dankeschön richtet sich an Luzie für ihre unermüdliche und aufopferungsvolle Liebe und Unterstützung, die all dies überhaupt erst möglich gemacht hat, in schönen wie in schweren Zeiten. Ich danke herzlich meiner lieben Familie, die mich von klein auf auf meinem Weg begleitet und unterstützt hat. Vielmals danken möchte ich Prof. Dr.-Ing. Steffen Marburg für die Betreuung dieser Arbeit und die zahlreichen fruchtbaren Diskussionen und Impulse, die mich immer wieder den roten Faden finden ließen. Danke Dir, lieber Steffen, für die vielen Gelegenheiten, die Welt zu bereisen und viele interessante Menschen kennen zu lernen, für die Freiheiten und das Vertrauen. Many thanks to Prof. Dr. Andrés Prieto for supervising my thesis and being a very friendly and helpful discussion partner. I enjoyed meeting you in A Coruña and hope to see you again soon in Munich. Furthermore, I would like to thank Prof. Dr. Carlo Bottasso for his guidance through the exam and for his friendly chairmanship. Many greetings to Sydney, namely to Prof. Dr. Nicole Kessissoglou and Dr. Daipei David Liu at UNSW, as well as to Dr. Herwig Peters. Best thanks for the wonderful time in “Down Under” and for the great introduction to the research topic. Ganz besonders möchte ich allen Weggefährt:innen an der UniBW und der TU München für die Unterstützung, tolle Zusammenarbeit und schöne Zeit danken, vor allem den “alten Hasen”, die von Anfang an dabei waren: Marcus Mäder, Patrick Langer, Christian Geweth, Theo Kiesel, Johannes Henneberg, Monika Gatt und Kheirollah Sepahvand. Aber natürlich auch jenen, die später an der TUM dazu gestoßen sind, u.a. Ferina Saati, Magdalena Scholz, Caglar Gürbüz, Felix Kronowetter, Martin Eser, Koji Baydoun, Christopher Jelich, Alex Hoppe, Anton Melnikov sowie Jonas und Johannes Schmid (nicht zu vergessen die immer hilfsbereiten Kolleginnen aus dem Sekretariat Elke Reichardt und Martina Sommer). Ich freue mich sehr, viele von euch als Freundinnen und Freunde gewonnen zu haben. Lasst uns in Kontakt bleiben! Gewidmet dem größten HF aller Zeiten VI Attached Publications [A] MOHEIT, L. & MARBURG, S. (2017). Infinite elements and their influence on normal and radiation modes in exterior
Recommended publications
  • A Review of Finite Element Methods for Time-Harmonic Acoustics
    L.L.Thompson: Finite element methods for acoustics, Preprint: J.Acoust.Soc.Am. A review of ¯nite element methods for time-harmonic acoustics Lonny L. Thompson Department of Mechanical Engineering, Clemson University Clemson, South Carolina, 29634-0921, USA Email: [email protected] (Dated: Submitted July 8, 2004; Resubmitted May 28, 2005; Revised Dec 10, 2005; Accepted Dec 12, 2005) PACS numbers: 43.20.Bi,43.20.Fn,43.20.Rz Keywords: acoustics; Helmholtz equation; ¯nite element method; stabilized methods; unbounded domains; absorbing boundary condition; nonreflecting boundary condition; absorbing layer; in¯nite element; complex- symmetric; domain decomposition method; adaptive method; a posteriori error estimate; inverse scattering; optimization 1 Abstract State-of-the-art ¯nite element methods for time-harmonic acoustics governed by the Helmholtz equation are reviewed. Four major current challenges in the ¯eld are speci¯cally addressed: the e®ective treatment of acoustic scattering in unbounded domains, including local and nonlocal absorbing boundary conditions, in¯nite elements, and absorbing layers; numerical dispersion errors that arise in the approximation of short unresolved waves, pol- luting resolved scales, and requiring a large computational e®ort; e±cient algebraic equation solving methods for the resulting complex-symmetric (non-Hermitian) matrix systems in- cluding sparse iterative and domain decomposition methods; and a posteriori error estimates for the Helmholtz operator required for adaptive methods. Mesh resolution to control phase error and bound dispersion or pollution errors measured in global norms for large wave numbers in ¯nite element methods are described. Stabilized, multiscale and other wave- based discretization methods developed to reduce this error are reviewed.
    [Show full text]
  • Performance Study of Plane Wave Finite Element Methods with a Padé
    Performance study of plane wave finite element methods with a Padé-type artificial boundary condition in acoustic scattering Ryiad Kerchroud, Azzedine Soulaimani, Xavier Antoine To cite this version: Ryiad Kerchroud, Azzedine Soulaimani, Xavier Antoine. Performance study of plane wave finite element methods with a Padé-type artificial boundary condition in acoustic scattering. Advances in Engineering Software, Elsevier, 2009, 40 (8), pp.738-750. 10.1016/j.advengsoft.2008.12.016. hal- 00591438 HAL Id: hal-00591438 https://hal.archives-ouvertes.fr/hal-00591438 Submitted on 9 May 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Performance study of plane wave finite element methods with a Pad´e-type artificial boundary condition in acoustic scattering R. Kechroud∗, A. Soulaimani∗, X. Antoine†‡ Abstract The aim of this paper is to propose and numerically study the performance of coupling a high-order Pad´e-type non-reflecting boundary condition with plane wave finite element formulations for solving high-frequency scattering problems involving elongated scatterers. It is shown on some numerical examples that the approximate solution can be obtained using a small number of degrees of freedom for a suitable accuracy.
    [Show full text]
  • Wave Propagation and Scattering, Inverse Problems, and Applications in Energy and the Environment November 21-25, 2011
    Workshop on Wave Propagation and Scattering, Inverse Problems, and Applications in Energy and the Environment November 21-25, 2011 as part of the Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment The efficient computation of wave propagation and scattering is a core problem in numerical mathematics, which is currently of great research interest and is central to many applications in energy and the envi- ronment. Two generic applications which resonate strongly with the central aims of this special semester are forward wave propagation in heterogeneous media and seismic inversion for subsurface imaging. As an example of the first application, modelling of absorption and scattering of radiation by clouds, aerosol and precipitation is used as a tool for interpretation of (e.g.) solar, infrared and radar measurements, and as a component in larger weather/climate prediction models in numerical weather forecasting. One key numerical component in this modelling is the prediction of the total optical properties and the full scattering matrix from an ensemble of irregular particles. The underlying mathematical problem is that of accurately computing high frequency wave propagation in a highly heterogeneous medium. As an example of the second application, inverse problems in wave propagation in heterogeneous media arise in the problem of imaging the subsurface below land or marine deposits. Solutions to this problem have a number of environmental uses, for example in the location of hydrocarbon-bearing rocks, in the mon- itoring of pollution in groundwater or in earthquake modelling. A seismic source is directed into the ground and the material properties of the subsurface are inferred by analysing the observed scattered field, recorded by sensors.
    [Show full text]
  • 2 Acoustic and Elastic Wave Equations
    ABSTRACT Mönkölä, Sanna Numerical Simulation of Fluid-Structure Interaction Between Acoustic and Elastic Waves Jyväskylä: University of Jyväskylä, 2011, 136 p. (Jyväskylä Studies in Computing ISSN 1456-5390; 133) ISBN 978-951-39-4438-4 (nid.) ISBN 978-951-39-4439-1 (PDF) Finnish summary Diss. This study considers developing numerical solution techniques for the computer sim- ulations of the fluid-structure interaction. The focus is especially on the efficiency of the iterative methods based on exact controllability and spectral element methods. In particular, the thesis concentrates on the coupling between two linear wave equations: the scalar-valued equation concerning the propagation of acoustic waves and the vector- valued equation modeling the propagation of waves in an elastic medium. These funda- mental equations occur in a number of physical applications, such as acoustics, medical ultrasonics, and geophysics. We consider both transient and time-harmonic problems. Traditionally, the com- plex-valued time-harmonic equations and low-order finite elements are used for solving the time-harmonic problems. This leads to large-scale indefinite systems, for which it is challenging to develop efficient iterative solution methods. Taking account of these diffi- culties, we turn to time-dependent equations. It is known that time-dependent equations can be simulated with respect to time until a time-harmonic solution is reached, but the approach suffers from poor convergence. Thus, we accelerate the convergence rate by employing the exact controllability method. The problem is formulated as a least-squares optimization problem, which is solved with the conjugate gradient (CG) algorithm. Com- putation of the gradient of the functional is done directly for the discretized problem.
    [Show full text]
  • Boundary Integral Equations Methods in Acoustic Scattering
    Boundary Integral Equations Methods in Acoustic Scattering A. Bendali Mathematical Institute, INSA, Toulouse and CERFACS, Toulouse M. Fares CERFACS, Toulouse February 28, 2007 1 Abstract The main subject of this contribution is to present some recent methods, specially designed to be implemented on parallel platforms, to deal with acoustic scattering problems involving a bounded zone filled by a heterogeneous medium. The main ap- proach is to couple a Finite Element Method, for handling this zone, with a Boundary Integral Equation, specially adapted to treat the unbounded part of the computational domain. After giving a short review of some alternative methods, we focus on the methods based on this approach and give a framework which makes it possible to construct almost all the standard Boundary Integral Equations. As well-known, each instance of this kind of scattering problems can be solved by a manifold of such equa- tions. This framework allows one to have a good insight into the advantages and the drawbacks of each of them. It is seen next that the above coupling gives rise to non standard linear systems, with a matrix being partly sparse and partly dense. Serious difficulties then arise when the solution of such systems has to be tackled on a parallel platform. It is shown how techniques from domain decomposition methods can be used to efficiently overcome these difficulties. Keywords: Acoustic Scattering, Helmholtz equation, Boundary Integral Equations, Finite Element Method, Coupling, Domain Decomposition Method, Cross-points. 1 Typical scattering problems in acoustics and brief review of some approaches to their numerical solu- tion The first part of this section is devoted to state some examples of scattering problems in acoustics.
    [Show full text]
  • Analysis of a Special Immersed Finite Volume Method for Elliptic Interface Problems
    INTERNATIONAL JOURNAL OF c 2019 Institute for Scientific NUMERICAL ANALYSIS AND MODELING Computing and Information Volume 16, Number 6, Pages 964{984 ANALYSIS OF A SPECIAL IMMERSED FINITE VOLUME METHOD FOR ELLIPTIC INTERFACE PROBLEMS KAI LIU AND QINGSONG ZOU Abstract. In this paper, we analyze a special immersed finite volume method that is different from the classic immersed finite volume method by choosing special control volumes near the interface. Using the elementwise stiffness matrix analysis technique and the H1-norm-equivalence between the immersed finite element space and the standard finite element space, we prove that the special finite volume method is uniformly stable independent of the location of the interface. Based on the stability, we show that our scheme converges with the optimal order O(h) in the H1 space and the order O(h3=2) in the L2 space. Numerically, we observe that our method converges with the optimal convergence rate O(h) under the H1 norm and with the the optimal convergence rate O(h2) under the L2 norm all the way even with very small mesh size h, while the classic immersed finite element method is not able to maintain the optimal convergence rates (with diminished rate up to O(h0:82) for the H1 norm error and diminished rate up to O(h1:1) for L2-norm error), when h is getting small, as illustrated in Tables 4 and 5 of [35]. Key words. Immersed finite volume method, stability, optimal convergence rates, immersed finite element method. 1. Introduction Interface problem is a kind of problem whose domain is typically separated by some curves or surfaces.
    [Show full text]
  • Hybrid Discontinuous Galerkin Methods for the Wave Equation
    DISSERTATION Hybrid Discontinuous Galerkin Methods for the Wave Equation ausgeführt zum Zwecke der Erlangung des akademischen Grades eines Doktors der technischen Wissenschaften unter der Leitung von Univ.-Prof. Dipl.-Ing. Dr.techn. Joachim Schöberl E101 Institut für Analysis und Scientific Computing eingereicht an der Technischen Universität Wien bei der Fakultät für Mathematik und Geoinformation von Dipl.-Ing. Martin Huber Matrikelnummer: 0056265 Wilhelmstraße 5/3 1120 Wien Wien, am 27. Februar 2013 i Kurzfassung Beim Lösen der Wellengleichung mit klassischen Finiten Elementen wächst für hohe Frequenzen ! die Anzahl der für eine vorgegebene Genauigkeit benötigten Unbekannten aufgrund des sogenannten „pollution effects“ stärker als O(!d) mit d als Raumdimension an. Als eine Möglichkeit dieses Problem in den Griff zu bekommen, werden in der vor- liegenden Dissertation hybride Discontinuous Galerkin Methoden für die skalare und die vektorwertige Wellengleichung vorgestellt. Üblicherweise beruhen klassische Finite Element Methoden (FEM) auf stetigen Ansatz- funktionen, während Discontinuous Galerkin Verfahren Basisfunktionen verwenden, die über Elementgrenzen hinweg unstetig sind. Erst zusätzliche Strafterme führen hier zu einer stetigen Lösung. Hybride FEMen basieren auf den selben Ansatzräumen, nur wird jetzt die Stetigkeit über zusätzliche Lagrangevariablen, die nur auf den Elementgrenzen leben, erzwungen. Im Falle der Wellengleichung ermöglicht die Einführung eines zweiten Satzes von Lagrangevariablen eine vollständige Elimination der ursprünglichen Freiheits- grade. Dadurch kann das Problem auf ein viel kleineres, nur für die Lagrangevariablen reduziert werden. Werden Finite Elemente zum Lösen eines auf einem unendlichen Gebiet gestellten Problems verwendet, wird in der Regel das Rechengebiet eingeschränkt, was transpar- ente Randbedingungen am neu entstandenen künstlichen Rand nötig macht. Als Real- isierungsmöglichkeiten für solche Randbedingungen werden sowohl die Hardy-Raum Meth- ode als auch eine Zerlegung des Fernfeldes in ebene Wellen diskutiert.
    [Show full text]
  • Andrés Prieto Aneiros
    Andr´es Prieto Aneiros PhD Dissertation SOME CONTRIBUTIONS IN TIME-HARMONIC DISSIPATIVE ACOUSTIC PROBLEMS Departamento de Matem´atica Aplicada Facultade de Matem´aticas ¿C´omo me vas a explicar, di, la dicha de esta tarde, si no sabemos porqu´e fue, ni c´omo, ni de qu´e ha sido, si es pura dicha de nada? En nuestros ojos visiones, visiones y no miradas, no percib´ıan tama˜nos, datos, colores, distancias. Pedro Salinas Contents Preface v I Porous materials 1 1 Porous models 3 1.1 Introduction .................................... 4 1.2 Rigid porous models ............................... 6 1.2.1 Darcy’s like model ............................ 7 1.2.2 Allard-Champoux model ......................... 13 1.3 Poroelastic models ................................ 15 1.3.1 Classical Biot’s model .......................... 15 1.3.2 Non-dissipative poroelastic model (closed pores) ............ 18 1.3.3 Non-dissipative poroelastic model (open pores) ............. 21 1.3.4 Dissipative poroelastic model (open pore) . .............. 22 2 Finite element solution of acoustic propagation in rigid porous media 25 2.1 Introduction .................................... 26 2.2 Models for fluid-porous vibrations ........................ 27 2.3 Associated nonlinear eigenvalue problems .................... 30 2.4 Statement of the weak formulation ....................... 34 2.5 Finite element discretization ........................... 35 2.6 Matrix description ................................ 37 2.7 Numerical results ................................. 38 2.8 Conclusions .................................... 41 3 Finite element solution of new displacement/pressure poroelastic models in acoustics 43 3.1 Introduction .................................... 44 3.2 Statement of the problem ............................ 44 3.3 Weak formulation ................................. 47 3.4 Finite element discretization ........................... 48 3.5 Matricial description ............................... 51 i ii Contents 3.6 Numerical solution of cell problems ......................
    [Show full text]
  • Beam-Tracing Domain Decomposition Method for Urban Acoustic Pollution
    Beam-tracing domain decomposition method for urban acoustic pollution Guillaume Gbikpi-Benissan∗ Frédéric Magoulès∗ Abstract This paper covers the fast solution of large acoustic problems on low-resources parallel platforms. A domain decomposition method is coupled with a dynamic load balancing scheme to efficiently accelerate a geometrical acoustic method. The geometrical method studied implements a beam-tracing method where intersections are handled as in a ray-tracing method. Beyond the distribution of the global processing upon multiple sub-domains, a second parallelization level is operated by means of multi-threading and shared memory mechanisms. Numerical experiments show that this method allows to handle large scale open domains for parallel computing purposes on few machines. Urban acoustic pollution arrising from car traffic was simulated on a large model of the Shinjuku district of Tokyo, Japan. The good speed-up results illustrate the performance of this new domain decomposition method. Keywords: Domain decomposition methods; Parallel and distributed computing; Acous- tics; Ray-tracing methods; Beam-tracing methods 1 Introduction Important material resources is often a requirement, either for the processing of large volumes of data, or for the fast resolution of large problems. Especially in parallel computing, the effectiveness of the designed algorithms is related to their scaling behavior on massively parallel platforms. However, for a great part of the scientific community, there remains a need for big simulations with very low resources. Then, it could be of major interest to design algorithms with good acceleration properties on very small clusters of machines. In this study, we tackle the simulation of car traffic noise level at a whole district scale.
    [Show full text]
  • Spectral-Infinite-Element Simulations of Gravity Anomalies
    Spectral-infinite-element simulations of gravity anomalies Item Type Article Authors Gharti, Hom Nath; Tromp, Jeroen; Zampini, Stefano Citation Gharti HN, Tromp J, Zampini S (2018) Spectral-infinite- element simulations of gravity anomalies. Geophysical Journal International 215: 1098–1117. Available: http://dx.doi.org/10.1093/ GJI/GGY324. Eprint version Publisher's Version/PDF DOI 10.1093/GJI/GGY324 Publisher Oxford University Press (OUP) Journal Geophysical Journal International Rights This is a pre-copyedited, author-produced PDF of an article accepted for publication in Geophysical Journal International following peer review. The version of record is available online at: https://academic.oup.com/gji/article/215/2/1098/5067876. Download date 05/10/2021 10:39:07 Link to Item http://hdl.handle.net/10754/629951 Geophys. J. Int. (2018) 215, 1098–1117 doi: 10.1093/gji/ggy324 Advance Access publication 2018 August 07 GJI Gravity, geodesy and tides Spectral-infinite-element simulations of gravity anomalies Downloaded from https://academic.oup.com/gji/article-abstract/215/2/1098/5067876 by King Abdullah University of Science and Technology user on 19 November 2018 Hom Nath Gharti,1 Jeroen Tromp1,2 and Stefano Zampini3 1Department of Geosciences, Princeton University, Princeton, New Jersey, USA. E-mail: [email protected] 2Program in Applied & Computational Mathematics, Princeton University, Princeton, New Jersey, USA 3Extreme Computing Research Center Computer, Electrical and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia Accepted 2018 August 3. Received 2018 July 29; in original form 2018 February 02 SUMMARY Gravity anomalies induced by density heterogeneities are governed by Poisson’s equation.
    [Show full text]
  • Toward Hp-Adaptive Solution of 3D Electromagnetic Scattering from Cavities
    An IntemationalJournal Available online at www.sciencedirectcom computers& .~,..~.@°,..~. mathematics with applications ELSEVIER Computers and Mathematics with Applications 49 (2005) 23-38 www.elsevier.com/locate/camwa Toward hp-Adaptive Solution of 3D Electromagnetic Scattering from Cavities A. ZDUNEK* Swedish Defence Research Agency FOI, Aeronautics Division (FFA) Computational Physics Department, SE-172 90 Stockholm, Sweden zka©foi, se W. RACHOWICZ t Institute for Computer Modelling, Section of Applied Mathematics Cracow University of Technology, P1 31-155 Cracow, Poland waldek©mlody, zms. pk. edu. pl N. SEHLSTEDT* Swedish Defence Research Agency FOI, Aeronautics Division (FFA) Computational Physics Department, SE-172 90 Stockholm, Sweden stn~foi.se (Received and accepted September 2003) Abstract--An effective hp-adaptive finite-element (FE) approach is presented for a reliable and accurate solution of 3D electromagnetic scattering problems. The far field is approximated with the infinite-element method. This allows one to reduce the external domain (discretised with finite elements) to a minimum preserving the possibility of arbitrary reduction of the error as the method does not introduce modelling error. The work is focused on scattering from cavity backed apertures recessed in a ground plane. Near optimal discretisations that can effectively resolve local rapid variations in the scattered field can be obtained adaptively by local mesh refinements (so called h- type refinements) blended with graded polynomial enrichments (p-enrichments). The discretisation error can be controlled by a self-adaptive process, which is driven by a posteriori error estimates in terms of the energy norm or in a quantity of interest. The radar cross section (RCS) is an example of the latter, h- and p-adaptively constructed solutions are compared to pure uniform p approximations.
    [Show full text]
  • Development of an Infinite Element Boundary to Model Gravity For
    University of Birmingham Development of an infinite element boundary to model gravity for subsurface civil engineering applications Haji, Twana; Faramarzi, Asaad; Metje, Nicole; Chapman, David; Rahimzadeh, Farough DOI: 10.1002/nag.3027 License: Creative Commons: Attribution (CC BY) Document Version Publisher's PDF, also known as Version of record Citation for published version (Harvard): Haji, T, Faramarzi, A, Metje, N, Chapman, D & Rahimzadeh, F 2019, 'Development of an infinite element boundary to model gravity for subsurface civil engineering applications', International Journal for Numerical and Analytical Methods in Geomechanics. https://doi.org/10.1002/nag.3027 Link to publication on Research at Birmingham portal General rights Unless a licence is specified above, all rights (including copyright and moral rights) in this document are retained by the authors and/or the copyright holders. The express permission of the copyright holder must be obtained for any use of this material other than for purposes permitted by law. •Users may freely distribute the URL that is used to identify this publication. •Users may download and/or print one copy of the publication from the University of Birmingham research portal for the purpose of private study or non-commercial research. •User may use extracts from the document in line with the concept of ‘fair dealing’ under the Copyright, Designs and Patents Act 1988 (?) •Users may not further distribute the material nor use it for the purposes of commercial gain. Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document. When citing, please reference the published version.
    [Show full text]