School of Mathematics and Statistics - Computational Maths
https://www.maths.unsw.edu.au/category/school-seminar-series/computational-maths
enOptimal control in stochastic Landau-Lifshitz-Gilbert equation
https://www.maths.unsw.edu.au/seminars/2017-09/optimal-control-stochastic-landau-lifshitz-gilbert-equation
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Ananta K. Majee</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">University of Tübingen, Germany</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Tue, 12/09/2017 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">CLB-1, Central Lecture Block, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p>In this presentation, we study an optimal control problem for the stochastic Landau-Lifshitz-Gilbert equation on a bounded domain in R^d (d = 1, 2, 3). We first establish existence of a relaxed optimal control for the relaxed version of the problem. As the control acts linearly in the equation, we then establish existence of an optimal control for the underlying problem. Furthermore, convergence of a structure preserving finite element approximation for d = 1 and physically relevant computational studies will be discussed.</p></div></div></section><div class="field field-name-field-seminar-latex field-type-text-long field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><div class="field field-name-field-seminar-url field-type-link-field field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/computational-maths">Computational Maths</a></li></ul></section>Thu, 07 Sep 2017 01:14:25 +0000z97015644340 at https://www.maths.unsw.edu.auSome finite element methods for the three-field formulation of elasticity
https://www.maths.unsw.edu.au/seminars/2017-09/some-finite-element-methods-three-field-formulation-elasticity
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Bishnu Lamichhane </div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">University of Newcastle, Australia.</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Tue, 19/09/2017 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">CLB-1, Central Lecture Block, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p>We consider a three-field formulation of linear elasticity problem. The standard three-field formulation -- often known as <br />the Hu-Washizu formulation in elasticity -- is the mother of many different finite element methods in engineering computation. We present some modified three-field formulations and their performance in removing locking effect in the nearly incompressible elasticity. The stabilisation of the standard three-field formulation is used to obtain the stabilised nodal strain formulation or node-based uniform strain elements. However, we show that standard or stabilised nodal strain formulation should be modified to have a uniformly convergent finite element approximation in the nearly incompressible case. We also consider an extension of the three-field formulation to a nonlinear case. </p></div></div></section><div class="field field-name-field-seminar-latex field-type-text-long field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><div class="field field-name-field-seminar-url field-type-link-field field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/computational-maths">Computational Maths</a></li></ul></section>Thu, 07 Sep 2017 00:53:36 +0000z97015644339 at https://www.maths.unsw.edu.auA study of constrained Navier-Stokes equations and related problems
https://www.maths.unsw.edu.au/seminars/2017-08/study-constrained-navier-stokes-equations-and-related-problems
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Gaurav Dhariwal</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">University of York, UK</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Tue, 22/08/2017 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">CLB-1, Central Lecture Block, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p>The talk will be divided in two parts: In the first part I will talk about deterministic and stochastic Navier-Stokes equations with a constraint on the L 2 energy of the solution. I will speak about the existence and the uniqueness of local strong solutions and the existence of a global solutions for the constrained 2D Navier-Stokes equations. So far we have been able to show the latter only on the torus and on the whole Euclidean space.</p>
<p>In the second part of the talk I will focus on the tamed 3D Navier-Stokes equations which was introduced by Röckner and Zhang [2, 3]. They proved the existence of a unique strong solution to a stochastic tamed 3D Navier-Stokes equation in the whole space and for the periodic boundary conditions case, using a result from Stroock and Varadhan [4]. We have found an alternative self contained approach based on a different approximation scheme and Skorohod-Jakubowski Theorem [1]. We also proved the existence of invariant measures in the whole space for damped equations.</p>
<p><strong>References</strong></p>
<p>[1] Z. Brzeźniak and E. Motyl, Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D-domains, J. Differential Equations, 254(4), 1627-1685 (2013).</p>
<p>[2] M. Röckner and X. Zhang, Tamed 3D Navier-Stokes Equation: Existence, Uniqueness and Regularity, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 12(4), 525-549 (2009).</p>
<p>[3] M. Röckner and X. Zhang, Stochastic Tamed 3D Navier-Stokes Equation: Existence, Uniqueness and Ergodicity, Probab. Theory Relat. Fields, 145, 211-267 (2009).</p>
<p>[4] D.W. Stroock and S.R.S. Varadhan, Multidimensional Diffusion Proceses, Springer, Berlin (1979).</p>
<p> </p>
<p> </p></div></div></section><div class="field field-name-field-seminar-latex field-type-text-long field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><div class="field field-name-field-seminar-url field-type-link-field field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/computational-maths">Computational Maths</a></li></ul></section>Wed, 16 Aug 2017 01:02:06 +0000z97015644316 at https://www.maths.unsw.edu.auLow-frequency excitation in unbounded 3D dielectric media: Formulation, analysis and applications
https://www.maths.unsw.edu.au/seminars/2017-08/low-frequency-excitation-unbounded-3d-dielectric-media-formulation-analysis-and
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">M. Ganesh</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">Colorado School of Mines, USA</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Tue, 08/08/2017 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">CLB-1, Central Lecture Blocks, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><pre>We consider electromagnetic wave propagation in three dimensional (3D) unbounded dielectric media governed by the Maxwell partial differential equations (PDE), radiation and interface conditions. The piecewise constant PDE coefficients are such that the continuous PDE model is well-posed for all frequencies, and as the frequency tends to zero, the electric and magnetic fields uncouple gracefully. It was an open problem to develop an equivalent bounded surface integral equation (SIE) model (based only on integral operators) and prove that the SIE does not from spurious resonances
and low-frequency breakdown. In this talk, we discuss our (surface currents and charges based) solution to this challenging reformulation and analysis problem, and briefly explore its applications using associated forward and inverse uncertain quantification models.</pre></div></div></section><div class="field field-name-field-seminar-latex field-type-text-long field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><div class="field field-name-field-seminar-url field-type-link-field field-label-hidden view-mode-rss"><div class="field-items"><div class="field-item even"></div></div></div><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/computational-maths">Computational Maths</a></li></ul></section>Tue, 01 Aug 2017 04:20:36 +0000z97015644301 at https://www.maths.unsw.edu.auThe multiscale regularizing method for solving Ill-posed problems
https://www.maths.unsw.edu.au/seminars/2017-08/multiscale-regularizing-method-solving-ill-posed-problems
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Min Zhong</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">Southeast University, Nanjing, PR China</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Tue, 15/08/2017 - 11:05am</span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">CLB-1, Central Lecture Block, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p>Using compactly supported radial basis functions (CSRBFs) of varying radii, Sloan, Wendland and LeGia have shown how a multiscale analysis can be applied to the approximation of Sobolev functions on a bounded domain and on the unit sphere. Here, we examine the application of this analysis to the solution of linear moderately ill-posed problems using Support Vector Approach regularization. Motivated by existing CSRBF-based multiscale regression methods, the multiscale reconstruction for an ill-posed problem is constructed by a sequence of residual corrections, where different support radii are employed to accommodate different scales. Convergence proof for the case of noise-free data and noisy data are derived from an appropriate choice of the Vapnik’s cut-off parameter and the regularization parameter. Numerical examples are constructed to verify the efficiency of the proposed approach and the effectiveness of the parameter choices.</p></div></div></section><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/computational-maths">Computational Maths</a></li></ul></section>Mon, 17 Jul 2017 01:26:18 +0000z97015644279 at https://www.maths.unsw.edu.auThe Guide to the Expression of Uncertainty in Measurement - Bayes, doped horses and chemistry
https://www.maths.unsw.edu.au/seminars/2017-03/guide-expression-uncertainty-measurement-bayes-doped-horses-and-chemistry
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Emeritus Professor D Brynn Hibbert FRSN</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">School of Chemistry, UNSW </div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Tue, 02/05/2017 - <span class="date-display-range"><span class="date-display-start">11:05am</span> to <span class="date-display-end">11:55am</span></span></span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even"> Rupert Myers Theatre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p>The seminar will be descriptions of an eclectic mix of mathematical and statistical methods applied in chemistry, with the unifying theme that the author has had a hand in each of them.</p>
<p lang="en-AU" xml:lang="en-AU">The Guide to the Expression of Uncertainty in Measurement (1) is published by Working Group 1 of the Joint Committee for Guides on Metrology, a group on which the author represented Chemistry (through IUPAC) from 2007-2015. Last revised in 2008, the committee has been working to prepare an edition for 2017. Evaluation of measurement uncertainty can be complex and is done in a quasi-Bayesian way, but the results are vital for the interpretation of measurement results in trade, health, forensics and the environment. The problem is to maintain rigour while providing methodology that can be used by practitioners.</p>
<p lang="en-AU" xml:lang="en-AU">A current topic of discussion, without any great outcomes, is how to treat the uncertainty of the determination of nominal properties, for example the identification of a drug, which can be seen as occupying a position in a multidimensional space defined by its atoms and their linkages. The analogue drug laws will be discussed and a question will be asked (2).</p>
<p lang="en-AU" xml:lang="en-AU">Analysing chemical data in racing animals is done to obtain regulatory limits of chemicals such as cobalt and carbon dioxide (3) by determining levels at which, for a ‘typical’ animal, the probability is ‘essentially zero’. Tracking drugs of abuse from the analysis of stable isotopes (13C, 2H, 15N) has allowed authorities to track illicit ice manufacture, and curtail the use of testosterone abuse in athletes. Methamphetamine data was classified done using expectation maximisation in a Gaussian mixture model (4).</p>
<p lang="en-AU" xml:lang="en-AU">1. Joint Committee for Guides in Metrology JCGM 100: Evaluation of measurement data - Guide to the expression of uncertainty in measurement; BIPM: Sèvres, 2008.</p>
<p>2. Hibbert, D. B.; Sutton, J., A chemical view of analogue drug laws in Australia. What is structural similarity? Australian Journal of Forensic Sciences 2016, 1 - 21.</p>
<p>3. (a) Hibbert, D.; Armstrong, N.; Vine, J., Total CO2 measurements in horses: where to draw the line. Accred. Qual. Ass. 2011, 16 (7), 339-345; (b) Sutton, G. J.; Cawley, A.; Murphy, C.; Lau, M. L.; Hibbert, D. B., Factors influencing total carbon dioxide concentrations in plasma of thoroughbred and standardbred racehorses. Drug Testing and Analysis 2014, 6 (9), 936-943.</p>
<p>4. Salouros, H.; Sutton, G. J.; Howes, J.; Hibbert, D. B.; Collins, M., Measurement of Stable Isotope Ratios in Methylamphetamine: A Link to Its Precursor Source. Anal. Chem. 2013, 85 (19), 9400-9408.</p>
</div></div></section><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/computational-maths">Computational Maths</a></li></ul></section>Tue, 21 Mar 2017 00:21:39 +0000z89000074160 at https://www.maths.unsw.edu.auProbability, Algebras, Analysis, and Numerics
https://www.maths.unsw.edu.au/seminars/2017-03/probability-algebras-analysis-and-numerics
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Hermann G. Matthies</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">Institute of Scientific Computing, TU Braunschweig</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Tue, 14/03/2017 - <span class="date-display-range"><span class="date-display-start">3:05pm</span> to <span class="date-display-end">3:55pm</span></span></span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">RC-4082, The Red Centre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p>Probability theory was axiomatically built on the concept of measure by A. Kolmogorov in the early 1930s, giving the probability measure and the related integral as primary objects and random variables, i.e., measurable functions, as secondary. Not long after Kolmogorov ́s work, developments in operator algebras connected to quantum theory in the early 1940s lead to similar results in an approach where algebras of random variables and the expectation functional are the primary objects. Historically this picks up the view implicitly contained in the early probabilistic theory of the Bernoullis.</p>
<p>This algebraic approach allows extensions to more complicated concepts like non-commuting random variables and infinite dimensional function spaces, as it occurs, e.g., in quantum field theory, random matrices, and tensor-valued random fields. It not only fully recovers the measure-theoretic approach, but can extend it considerably. For much practical and numerical work, which is often primarily concerned with random variables, expectations, and conditioning, it offers an independent theoretical underpinning. In short words, it is “probability without measure theory”.</p>
<p>This functional analytic setting has also strong connections to the spectral theory of linear operators, where analogies to integration are apparent if they are looked for. These links extend in a twofold way to the concept of weak distribution, which describes probability on infinite dimensional vector spaces. Here the random elements are represented by linear mappings, and factorisations of linear maps are intimately connected with representations and tensor products, as they appear in numerical approximations.</p>
<p>Taking this conceptual basis of vector spaces, algebras, linear functionals, and operators gives a fresh view on the concepts of expectation and conditioning, as it occurs in applications of Bayes's theorem.</p></div></div></section><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/computational-maths">Computational Maths</a></li></ul></section>Sun, 05 Mar 2017 23:47:06 +0000z89000074138 at https://www.maths.unsw.edu.auDistributing points on spheres and other manifolds
https://www.maths.unsw.edu.au/seminars/2017-02/distributing-points-spheres-and-other-manifolds
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">Juan G. Criado del Rey</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">University of Cantabria</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Tue, 07/02/2017 - <span class="date-display-range"><span class="date-display-start">11:05am</span> to <span class="date-display-end">11:55am</span></span></span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">RC-4082, The Red Centre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><p>Distributing points on spheres or other sets is a very classical problem. Its modern formulation in terms of energy-minimising configurations is due to the discoverer of the electron J. J. Thomson who, in 1904, posed the question: <em> in which position within some set, such as a ball or a sphere, would N electrons lie in order to minimise their electrostatic potential?</em> There are many different approaches to the definition of what a <em>sensibly distributed</em> collection of spherical points is. Apart from the aforementioned minimisation of energy, other definitions include minimising the separation distance, having a small discrepancy, providing exact integral formulas for low degree polynomials, etc. In this talk we will review some of these problems and address the problem of defining minimal-energy points in an arbitrary compact manifold from an intrinsic viewpoint.</p></div></div></section><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/computational-maths">Computational Maths</a></li></ul></section>Sun, 29 Jan 2017 22:47:26 +0000z89000074080 at https://www.maths.unsw.edu.auSign-definite formulations and frequency-robust preconditioned FEMs: Part 2
https://www.maths.unsw.edu.au/seminars/2016-10/sign-definite-formulations-and-frequency-robust-preconditioned-fems-part-2
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">M. Ganesh</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">Colorado School of Mines</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Tue, 25/10/2016 - <span class="date-display-range"><span class="date-display-start">11:05am</span> to <span class="date-display-end">11:55am</span></span></span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">RC-4082, The Red Centre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><div class="field-items">
<div class="field-item even">
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<div>The standard Galerkin formulation of the acoustic wave propagation governed by the Helmholtz partial differential equation (PDE) is indefinite for large wavenumbers. However, the Helmholtz PDE is in general not indefinite. The lack of coercivity (indefiniteness) in the formulation and associated finite element method (FEM) models is one of the major difficulties for approximation and simulation of wave propagation models using iterative methods. </div>
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<div>This is the second of two talks on a new class of constructive preconditioned sign-definite FEM Helmholtz wave propagation models in homogeneous and heterogeneous media. The main focus of Part I was on the constant coefficient Helmholtz PDE. Part II will deal with heterogeneous media, coercive formulations and analysis. </div>
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<div>Our new preconditioned FEM formulations provide concrete answers to some key issues raised by the authors in a recent SIAM Review article about the practical use of their theoretical homogeneous media sign-definite formulation. Further, we remove the notion of sign-indefiniteness and frequency-sensitive iterations associated with heterogeneous media acoustic wave propagation models.</div>
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</div></div></div></section><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/computational-maths">Computational Maths</a></li></ul></section>Mon, 03 Oct 2016 22:38:39 +0000z89000073990 at https://www.maths.unsw.edu.auSign-definite formulations and frequency-robust preconditioned FEMs: Part 1
https://www.maths.unsw.edu.au/seminars/2016-10/sign-definite-formulations-and-frequency-robust-preconditioned-fems-part-1
<section class="field field-name-field-seminar-speaker field-type-text field-label-above view-mode-rss"><h2 class="field-label">Speaker: </h2><div class="field-items"><div class="field-item even">M. Ganesh</div></div></section><section class="field field-name-field-seminar-affiliation field-type-text field-label-above view-mode-rss"><h2 class="field-label">Affiliation: </h2><div class="field-items"><div class="field-item even">Colorado School of Mines</div></div></section><section class="field field-name-field-seminar-date field-type-date field-label-above view-mode-rss"><h2 class="field-label">Date: </h2><div class="field-items"><div class="field-item even"><span class="date-display-single">Tue, 11/10/2016 - <span class="date-display-range"><span class="date-display-start">11:05am</span> to <span class="date-display-end">11:55am</span></span></span></div></div></section><section class="field field-name-field-seminar-venue field-type-text field-label-above view-mode-rss"><h2 class="field-label">Venue: </h2><div class="field-items"><div class="field-item even">RC-4082, The Red Centre, UNSW</div></div></section><section class="field field-name-field-seminar-abstract field-type-text-long field-label-above view-mode-rss"><h2 class="field-label">Abstract: </h2><div class="field-items"><div class="field-item even"><div>
<div>The standard Galerkin formulation of the acoustic wave propagation governed by the Helmholtz partial differential equation (PDE) is indefinite for large wavenumbers. However, the Helmholtz PDE is in general not indefinite. The lack of coercivity (indefiniteness) in the formulation and associated finite element method (FEM) models is one of the major difficulties for approximation and simulation of wave propagation models using iterative methods. </div>
<div> </div>
<div>We will present (in two talks) a new class of constructive preconditioned sign-definite FEM Helmholtz wave propagation models in homogeneous and heterogeneous media. The main focus of Part I will be on the constant coefficient Helmholtz PDE; and Part II will deal with heterogeneous media, coercive formulations and analysis. </div>
<div> </div>
<div>Our new preconditioned FEM formulations provide concrete answers to some key issues raised by the authors in a recent SIAM Review article about the practical use of their theoretical homogeneous media sign-definite formulation. Further, we remove the notion of sign-indefiniteness and frequency-sensitive iterations associated with heterogeneous media acoustic wave propagation models.</div>
</div></div></div></section><section class="field field-name-taxonomy-vocabulary-4 field-type-taxonomy-term-reference field-label-above view-mode-rss"><h2 class="field-label">School Seminar Series: </h2><ul class="field-items"><li class="field-item even"><a href="/category/school-seminar-series/computational-maths">Computational Maths</a></li></ul></section>Mon, 03 Oct 2016 22:31:28 +0000z89000073989 at https://www.maths.unsw.edu.au