mathLab innovating with mathematics
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en Computational Methods for Optimal Control in Parabolic PDEs and Applications
http://mathlab.sissa.it/computational-methods-optimal-control-parabolic-pdes-and-applications
<div class="section field field-name-field-date-events field-type-datestamp field-label-inline clearfix"><h3 class="field-label">Date: </h3><div class="field-items"><div class="field-item odd"><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2017-08-30T15:00:00+02:00">Wednesday, 30 August, 2017 - 15:00</span></div></div></div><div class="section field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item odd" property="content:encoded"><p><strong>Speaker</strong>: Dr Efthymios Karatzas, SISSA mathLab</p>
<p><strong>Title</strong>: Computational Methods for Optimal Control in Parabolic PDEs and Applications</p>
<p><strong>Time</strong>: 3pm, August 30, 2017</p>
<p><strong>Place</strong>: room A-005 , SISSA main campus, Via Bonomea 265, 34136 Trieste</p>
<p><strong>Abstract:</strong> We discuss distributed and boundary optimal control problems related to parabolic partial differential equations using a discontinuous Galerkin time stepping scheme. In particular, we focus on a Robin boundary optimal control problem for linear parabolic equations, on a distributed optimal control problem for the evolutionary Stokes equations and on some nonlinear optimal control problems arising from Biology. Stability and error estimates are presented for schemes of arbitrary order, under suitable regularity assumptions on the given data. Using suitable projection techniques, we also analyze the case of non-smooth initial data. Finally, we present numerical examples that verify our theoretical findings, and we discuss computational challenges involved in the numerical solution of the above systems.</p>
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Thu, 21 Sep 2017 09:33:28 +0000giovannistabile374 at http://mathlab.sissa.itExtended-unfitted Nitsche finite element method for an elliptic PDE problem and applications
http://mathlab.sissa.it/extended-unfitted-nitsche-finite-element-method-elliptic-pde-problem-and-applications
<div class="section field field-name-field-date-events field-type-datestamp field-label-inline clearfix"><h3 class="field-label">Date: </h3><div class="field-items"><div class="field-item odd"><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2017-09-21T12:00:00+02:00">Thursday, 21 September, 2017 - 12:00</span></div></div></div><div class="section field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item odd" property="content:encoded"><div><strong>Speaker</strong>: Dr Efthymios Karatzas, SISSA mathLab<br /><strong>Where</strong>: Room A-133, SISSA main campus, Via Bonomea 265, Trieste
<div><strong>When</strong>: Thursday 21 September 2017, 12pm (till 1pm)</div>
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<div><strong>Abstract</strong>: We introduce and discuss the Nitsche finite element method for the simplest elliptic problem: the Poisson problem with Neumman and Dirichlet mixed boundary conditions, using an extended mesh, and cut boundary elements. We focus on the a posteriori error estimates with emphasis in the cases of a quantity of interest a linear functional in the interior and a functional related to the normal flux in the Dirichlet boundary. The a posteriori error representation Lemma's and the corresponding error optimal bounds are presented, and the related sketch proof is demonstrated. We examine the case of uncertainties in our problem for a quantity of interest and an application related to the failure probability of a PDE model with random data with some ways to reduce the computational cost.</div>
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Thu, 21 Sep 2017 09:30:14 +0000giovannistabile373 at http://mathlab.sissa.itReduced Order Methods: State of the Art and Perspectives with Focus on Computational Fluid Dynamics
http://mathlab.sissa.it/reduced-order-methods-state-art-and-perspectives-focus-computational-fluid-dynamics
<div class="section field field-name-field-date-events field-type-datestamp field-label-inline clearfix"><h3 class="field-label">Date: </h3><div class="field-items"><div class="field-item odd"><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2017-07-05T15:00:00+02:00">Wednesday, 5 July, 2017 - 15:00</span></div></div></div><div class="section field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item odd" property="content:encoded"><div><strong>Speaker:</strong> Gianluigi Rozza (SISSA)</div>
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<div><strong>Date and Venue: </strong>Wednesday, 5 July 2017, 15:00 - 17:00 SISSA main building, Lecture room A-128</div>
<p><strong>Abstract.</strong><strong> </strong>In this talk, we provide the state of the art of Reduced Order Methods (ROM) for parametric Partial Differential Equations (PDEs), and we focus on some perspectives in their current trends and developments, with a special interest in parametric problems arising in Computational Fluid Dynamics (CFD). Systems modelled by PDEs are depending by several complex parameters in need of being reduced, even before the computational phase in a pre-processing step in order to reduce parameter space. Efficient parametrizations (random inputs, geometry, physics) are very important to be able to properly address an offline-online decoupling of the computational procedures and to allow competitive computational performances. Current ROM developments in CFD include: a better use of stable high fidelity methods, such as parametric spectral element method, enhancing the quality of the reduced model too; the use of finite volume discretisation with turbulent models; more efficient sampling techniques to reduce the number of the basis functions, retained as snapshots, and the dimension of online systems; the improvements of the certification of accuracy based on residual based error bounds and stability factors, as well as the the guarantee of the stability of the approximation with proper space enrichment. For nonlinear systems, also the investigations on of bifurcations of parametric solutions are crucial and they may be obtained thanks to a reduced eigenvalue analysis. All the previous aspects are very important in CFD problems to be able to focus in real time on complex parametric industrial and biomedical flow problems or even in a control flow setting, and to couple viscous flows -velocity, pressure, as well as thermal field - with a structural field or a porous medium, thus requiring also an efficient reduced parametric treatment of interfaces between different physics. Model flow problems will focus on few benchmark cases in a time-dependent framework, as well as on fluid-structure interaction problems. The research has been carried out at SISSA mathLab within the ERC AROMA-CFD project.</p>
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Thu, 13 Jul 2017 07:17:09 +0000giovannistabile367 at http://mathlab.sissa.itOn the nonlocal curvatures of open surfaces
http://mathlab.sissa.it/nonlocal-curvatures-open-surfaces
<div class="section field field-name-field-date-events field-type-datestamp field-label-inline clearfix"><h3 class="field-label">Date: </h3><div class="field-items"><div class="field-item odd"><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2017-07-05T14:00:00+02:00">Wednesday, 5 July, 2017 - 14:00</span></div></div></div><div class="section field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item odd" property="content:encoded"><p class="rtejustify"><strong>Speaker</strong>: professor Paolo Podio-Guidugli, Accademia Nazionale dei Lincei/University of Rome Tor Vergata</p>
<p class="rtejustify"><strong>Room</strong>: A-133, SISSA Campus, Via Bonomea 265, Trieste</p>
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<p><strong>Abstract: </strong>There is a triple point of geometry, mechanics and mathematical analysis where three notions are met: the geometrical notion of mean curvature of a surface plays a pivotal role between the mechanical notion of diusion of a substance and the analytical notion of Laplacian of a scalar-valued function. Interestingly, this triple-point situation occurs also for nonlocal mean curvature, anomalous diusion, and fractional Laplacians [1]. So far, only closed surfaces have been considered, for which nonlocal directional and mean curvatures have been dened [2, 3]. I will discuss the analogous notions for open surfaces recently proposed in [4], which are based on a notion of area functional for this type of surfaces.</p>
<p><strong>References:</strong></p>
<p>[1] P. Podio-Guidugli, A notion of nonlocal Gaussian curvature. Rend. Lincei Mat. Appl. 27 (2016), 181-193.</p>
<p>[2] N. Abatangelo and E. Valdinoci, A notion of nonlocal curvature. Numer. Funct. Anal. Optim. 35 (2014), 793-815.</p>
<p>[3] X. Cabre, M.M. Fall, J. Sola-Morales, and T. Weth, Curves and surface with constant nonlocal mean curvature: meeting Alexandrov and Delauney. arXiv:1503.00469 [math.AP].</p>
<p>[4] R. Paroni, P. Podio-Guidugli, and B. Seguin, On the nonlocal curvatures of open surfaces. arXiv:1701.06513 [math.DG].</p>
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Mon, 26 Jun 2017 11:05:25 +0000Giovanni Noselli366 at http://mathlab.sissa.it Optimization-based Dynamic Mesh Algorithms for Use in Finite Element Simulations
http://mathlab.sissa.it/optimization-based-dynamic-mesh-algorithms-use-finite-element-simulations
<div class="section field field-name-field-date-events field-type-datestamp field-label-inline clearfix"><h3 class="field-label">Date: </h3><div class="field-items"><div class="field-item odd"><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2017-06-21T11:00:00+02:00">Wednesday, 21 June, 2017 - 11:00</span></div></div></div><div class="section field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item odd" property="content:encoded"><p><strong>Speaker</strong>: Prof. Suzanne Michelle Shontz, University of Kansas, USA</p>
<p><strong>Date and Time</strong>: Wednesday June 21st, 2017 at 11 am,</p>
<div><strong>Place:</strong> room A-134, SISSA main campus, Via Bonomea 265, 34136 Trieste, </div>
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<div>This seminar is in cooperation with the local <strong>SISSA</strong><strong> SIAM student chapter.</strong></div>
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<div><strong>Abstract: </strong></div>
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<p>There are numerous applications for which the geometric domain moves as a function of time, e.g., flapping airplane wings, a beating heart, and clothing moving in the wind. A dynamic sequence of meshes is required in order to capture the changing geometry. </p>
<p>In the first part of the talk, I will present parallel LBWARP, a parallel log barrier-based tetrahedral mesh warping algorithm for distributed memory machines. The algorithm is a general-purpose, geometric dynamic meshing algorithm that parallelizes the sequential LBWARP algorithm by Shontz and Vavasis. The algorithm solves a large global system of linear equations in parallel to determine where to move the interior nodes of the mesh. This computation is based on the representation of the initial mesh and the deformation provided by the user. A log-barrier interior point method is used to solve several convex optimization problems to determine the representation of the initial mesh. Sparse linear solvers for problems with multiple right-hand sides are used to solve the global systems of linear equations corresponding to multiple warping steps. I will present several numerical examples which demonstrate the excellent scalability properties of the method. </p>
<p>In the second part of the talk, I will present LBWARP2Gen, a high-order curvilinear tetrahedral mesh generation and warping algorithm. The algorithm generates a second-order mesh by deforming a linear tetrahedral mesh into a high-order mesh based on the LBWARP method. In particular, it first, adds a node at the midpoint of each edge; second, displaces the newly added boundary midpoints onto the curved boundary, and third, solves for the final positions of the interior nodes based on the boundary deformation (based on the representation of the initial high-order mesh and the mesh deformation). In this case, a log-barrier interior point method is used to solve the resulting nonconvex optimization problems. By allowing all of the boundary nodes to move, the approach can also be used to warp second-order tetrahedral meshes. I will present numerical examples which demonstrate the success of the method in generating and warping high-order meshes. </p>
<p> Parts of this talk represent joint work by Thap Panitanarak, The Pennsylvania State University, and Michael Stees, University of Kansas.</p>
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Wed, 21 Jun 2017 08:37:32 +0000giovannistabile365 at http://mathlab.sissa.itMorphogenesis and self-organization of cell aggregates
http://mathlab.sissa.it/morphogenesis-and-self-organization-cell-aggregates
<div class="section field field-name-field-date-events field-type-datestamp field-label-inline clearfix"><h3 class="field-label">Date: </h3><div class="field-items"><div class="field-item odd"><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2017-05-30T14:00:00+02:00">Tuesday, 30 May, 2017 - 14:00</span></div></div></div><div class="section field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item odd" property="content:encoded"><p><strong>Speaker</strong>: Dr Roberto Natalini<br /><strong>Affiliation</strong>: Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche</p>
<div><strong>Date</strong>: Tuesday, May 30, 2017</div>
<div><strong>Time</strong>: 2pm</div>
<div><strong>Place</strong>: Room A-005, SISSA main campus, Via Bonomea 265, 34136 Trieste</div>
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Abstract: In this talk we present a class of discrete in continuous mathematical models, which describe self-organization phenomena for some different classes of stem cells. Our models try to mimic the<br />
results obtained in recent biological experiments. We rely on a hybrid description: discrete for the cellular level and continuous for the molecular level. Two case studies are considered: the formation of neuromastes in the posterior lateral line of zebrafishes, and the growth of the so called cardiospheres, which are composed by the precursors of human cardiac cells. For a simple casy we prove the existence of steady solutions consistent with the formation of particular biological structure.</div>
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Thu, 25 May 2017 06:49:53 +0000giovannistabile364 at http://mathlab.sissa.it Finite Element Reduced Basis (Proper Orthogonal Decomposition) Approach for Geometrically Parametrized Stokes Flow
http://mathlab.sissa.it/finite-element-reduced-basis-proper-orthogonal-decomposition-approach-geometrically-parametrized
<div class="section field field-name-field-date-events field-type-datestamp field-label-inline clearfix"><h3 class="field-label">Date: </h3><div class="field-items"><div class="field-item odd"><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2017-05-18T10:00:00+02:00">Thursday, 18 May, 2017 - 10:00</span></div></div></div><div class="section field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item odd" property="content:encoded"><p><strong>Speaker</strong>: Nirav Shah's (University of Stuttgart) SISSA mathLab internal seminar.</p>
<p><strong>Time and place: </strong>Thursday May 18, 2017 at 10am Red meeting room Library.</p>
<p><strong>Abstract</strong> :</p>
<p dir="ltr">Stokes flow, also known as Viscous flow, has its application in the fields of mechanical engineering such as oil flow in journal bearing, aerodynamics such as flow around wings, environmental engineering such as groundwater flow and biomedical applications such as cardiovascular flows. All these flows are governed by incompressible stokes flow equation. The governing equations are solved numerically by method such as Finite Element Method(FEM). Rapid and economic evaluation of output has given rise to the parametrization of governing partial differential equation and subsequently, Reduced Basis(RB) methods. The presentation demonstrates the proper orthogonal decomposition based reduced order modelling of stokes flow in geometrically parametrized domain.</p>
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Wed, 17 May 2017 07:03:07 +0000giovannistabile363 at http://mathlab.sissa.itHierarchical model reduction techniques for flows in a parametric setting
http://mathlab.sissa.it/hierarchical-model-reduction-techniques-flows-parametric-setting
<div class="section field field-name-field-date-events field-type-datestamp field-label-inline clearfix"><h3 class="field-label">Date: </h3><div class="field-items"><div class="field-item odd"><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2017-05-18T16:30:00+02:00">Thursday, 18 May, 2017 - 16:30</span></div></div></div><div class="section field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item odd" property="content:encoded"><div>
<div><strong>Speaker</strong>: Matteo Zancanaro, Politecnico di Milano, pre-doc at SISSA mathLab</div>
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<div><strong>Date</strong>: May 18, 2017</div>
<div><strong>Time</strong>: 4:30pm</div>
<div><strong>Place:</strong> Room A-135, SISSA main campus, Via Bonomea 265, Trieste</div>
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<div><strong>Abstract</strong>: Nowadays, the fields where computational fluid dynamic is being applied are growing in number and importance very fast. Just to mention few applications, from aerospace to automotive ones, from architectural to environmental ones and only most recently medical ones to optimize some surgical interventions about cardiovascular or breathing apparatus. On the other hand, unfortunately, obtaining some useful results by solving fluid dynamic equations over complex domains, can be very difficult because of the processing power needed or computational time machine requested. This is why</div>
<div>during the last years it has been worked a lot in order to develop several new techniques able to solve this kind of problems in an easier way by accomplishing two goals: reduction of computational time needed and increment of the solution accuracy without augmenting the CPU power. In this work we would like to compare some of these techniques (RB, POD, HiMOD, HiPOD, HiRB) by the use of the finite element library FEniCS with a Python interface. </div>
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<div><strong>Joint work between SISSA mathLab and MOX-Politecnico di Milano.</strong></div>
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Tue, 16 May 2017 13:06:52 +0000giovannistabile362 at http://mathlab.sissa.itFinite element quasi-interpolation and best approximation
http://mathlab.sissa.it/finite-element-quasi-interpolation-and-best-approximation
<div class="section field field-name-field-date-events field-type-datestamp field-label-inline clearfix"><h3 class="field-label">Date: </h3><div class="field-items"><div class="field-item odd"><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2017-05-11T16:30:00+02:00">Thursday, 11 May, 2017 - 16:30</span></div></div></div><div class="section field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item odd" property="content:encoded"><p><strong>Speaker: Prof. Alexandre Ern, CERMICS, ENPC Paris-Tech and Ecole Polytechnique Paris, France</strong></p>
<div>Place: Room A-005, SISSA main Campus, Via Bonomea 265, Trieste</div>
<div>Time: 4:30PM</div>
<div>Date: Thursday, May 11, 2017</div>
<div><u><em>The seminar is also part of the activity of the local SISSA student SIAM chapter.</em></u></div>
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<div><strong>Title</strong> : Finite element quasi-interpolation and best approximation
<p>Abstract : We introduce quasi-interpolation operators for scalar- and vector-valued finite element spaces with some continuity across mesh interfaces. These operators are stable in L1, are projections, and deliver optimal local approximation estimates in Sobolev spaces. The theory is illustrated on H1-, H(curl)- and H(div)-conforming finite element spaces. This is joint work with J.-L. Guermond.</p></div>
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Sat, 06 May 2017 16:37:49 +0000giovannistabile361 at http://mathlab.sissa.itThe shifted Nitsche method: A new approach to embedded boundary conditions
http://mathlab.sissa.it/shifted-nitsche-method-new-approach-embedded-boundary-conditions-0
<div class="section field field-name-field-date-events field-type-datestamp field-label-inline clearfix"><h3 class="field-label">Date: </h3><div class="field-items"><div class="field-item odd"><span class="date-display-single" property="dc:date" datatype="xsd:dateTime" content="2017-05-09T16:00:00+02:00">Tuesday, 9 May, 2017 - 16:00</span></div></div></div><div class="section field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item odd" property="content:encoded"><div>
<p><strong>Speaker: Prof. Guglielmo Scovazzi, Duke University</strong></p>
<div>Place: Room A-005, SISSA main Campus, Via Bonomea 265, Trieste</div>
<div>Time: 4:00PM</div>
<div>Date: Tuesday, May 9, 2017</div>
<div><u><em>The seminar is also part of the activity of the local SISSA SIAM student chapter.</em></u></div>
<p><strong>Title: </strong><em>The shifted Nitsche method: A new approach to embedded boundary conditions</em></p>
<p><strong>Abstract: </strong>Embedded boundary methods obviate the need for continual re-meshing in many applications involving rapid prototyping and design. Unfortunately, many finite element embedded boundary methods for incompressible flow are also difficult to implement due to the need to perform complex cell-cutting operations at boundaries. We present a new, stable, and simple embedded boundary method, which we call “the shifted Nitsche method.” The proposed method eliminates the need to perform cell cutting, and demonstrate it on large-scale incompressible flow problems, solid mechanics, shallow water flows. </p>
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<div><strong>Biographical Sketch: </strong></div>
<div>Guglielmo Scovazzi earned B.S./M.S. Degrees in Aerospace Engineering at Politecnico di Torino in 1998. He received a M.S. in 2001 and a Ph.D. in 2004, both in Mechanical Engineering, from Stanford University. Between 2004 and 2012, he worked as Senior Member of the Technical Staff at Sandia National Laboratories, Albuquerque (New Mexico), and since August 2012, he is Associate Professor in the Civil & Environmental Engineering Department at Duke University, with a secondary appointment in the Mechanical Engineering and Materials Science Department. </div>
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<div>Guglielmo Scovazzi is a recipient of the 2014 Early Career Award from the Office of Science of the US Department Of Energy (ASCR program), and the 2017 PECASE award.</div>
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<div>His interests are in the general area of computational mechanics, and more specifically in computational fluids and solid mechanics, fluid/structure interaction, and flow through porous media. He is a member of the Editorial Board of the International Journal on Numerical Methods in Fluids, and a Member of SIAM and USACM. </div>
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Sat, 06 May 2017 16:36:10 +0000giovannistabile360 at http://mathlab.sissa.it