MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1253 products
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59/2017 - 11/03/2017
Grujic, O.; Menafoglio, A.; Guang, Y.; Caers, J.
Cokriging for multivariate Hilbert space valued random fields. Application to multifidelity computer code emulation | Abstract | | In this paper we propose Universal trace co-kriging (UTrCoK), a novel methodology for interpolation of multivariate Hilbert space valued functional data. Such data commonly arises in multi-fidelity numerical modeling of the subsurface and it is a part of many modern uncertainty quantification studies. Besides theoretical developments we also present methodological evaluation and comparisons with the recently published projection based approach by Bohorquez et al (2016). Our evaluations and analyses were performed on synthetic (oil reservoir) and real field (Uranium contamination) subsurface uncertainty quantification case studies. Monte Carlo analyses were conducted to draw important conclusions and to provide practical guidelines for all future practitioners. |
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58/2017 - 11/02/2017
Landajuela, M.; Vergara, C.; Gerbi, A.; Dede', L.; Formaggia, L.; Quarteroni, A.
Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network | Abstract | | In this work, we consider the numerical approximation of the electromechanical
coupling in the left ventricle with inclusion of the Purkinje network.
The mathematical model couples the 3D elastodynamics and bidomain
equations for the electrophysiology in the myocardium with the 1D
monodomain equation in the Purkinje network. For the numerical solution
of the coupled problem, we consider a fixed-point iterative algorithm that
enables a partitioned solution of the myocardium and Purkinje network
problems. Different levels of myocardium-network splitting are considered
and analyzed. The results are compared with those obtained using standard
strategies proposed in the literature to trigger the electrical activation. Finally,
we present a physiological cardiac simulation, including the initiation
of the signal in the Purkinje network, the systolic phase and the beginning
of the filling phase. |
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57/2017 - 10/31/2017
Ballarin, F.; D'Amario, A.; Perotto, S.; Rozza, G.
A POD-Selective Inverse Distance Weighting method for fast parametrized shape morphing | Abstract | | Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus on Inverse Distance Weighting (IDW) interpolation techniques, where a reference domain is morphed into a deformed one via the displacement of a set of control points. We aim at reducing the computational burden characterizing a standard IDW approach without compromising the accuracy. To this aim, first we propose an improvement of IDW based on a geometric criterion which automatically selects a subset of the original set of control points. Then, we combine this new approach with a model reduction technique based on a Proper Orthogonal Decomposition of the set of admissible displacements. This choice further reduces computational costs. We verify the performances of the new IDW techniques on several tests by investigating the trade-off reached in terms of accuracy and efficiency. |
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56/2017 - 10/31/2017
Alberti, G. S.; Santacesaria, M.
Infinite dimensional compressed sensing from anisotropic measurements | Abstract | | In this paper, we consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The main result gives explicit bounds on the number of measurements in order to achieve stable recovery, which depends on the mutual coherence of the two systems. As a simple corollary, we prove the efficiency of non-uniform sampling strategies in cases when the two systems are not incoherent, but only asymptotically incoherent, as with the recovery of wavelet coefficients from Fourier samples. This general framework finds applications to several inverse problems in partial differential equations, in which the standard assumptions of compressed sensing are not satisfied: several examples are discussed. |
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53/2017 - 10/23/2017
Bertagna, L.; Deparis, S.;Formaggia, L.; Forti, D.; Veneziani A.
The LifeV library: engineering mathematics beyond the proof of concept | Abstract | | LifeV is a library for the finite element (FE) solution of partial differential equations in one, two, and three dimensions. It is written in C++ and designed to run on diverse parallel architectures, including cloud and high performance computing facilities. In spite of its academic research nature, meaning a library for the development and testing of new methods, one distinguishing feature of LifeV is its use on real world problems and it is intended to provide a tool for many engineering applications. It has been actually used in computational hemodynamics, including cardiac mechanics and fluid-structure interaction problems, in porous media, ice sheets dynamics for both forward and inverse problems. In this paper we give a short overview of the features of LifeV and its coding paradigms on simple problems. The main focus is on the parallel environment which is mainly driven by domain decomposition methods and based on external libraries such as MPI, the Trilinos project, HDF5 and ParMetis.
(Dedicated to the memory of Fausto Saleri) |
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54/2017 - 10/23/2017
Dede', L; Quarteroni, A.
Isogeometric Analysis of a Phase Field Model for Darcy Flows with Discontinuous Data | Abstract | | We consider a phase field model for Darcy flows with discontinuous data in porous media; specifically, we adopt the Hele-Shaw-Cahn-Hillard equations of [Lee, Lowengrub, Goodman, Physics of Fluids, 2002] to model flows in the Hele-Shaw cell through a phase field formulation which incorporates discontinuities of physical data, namely density and viscosity, across interfaces. For the spatial approximation of the problem, we use NURBS-based Isogeometric Analysis in the framework of the Galerkin method, a computational framework which is particularly advantageous for the solution of high order Partial Differential Equations and phase field problems which exhibit sharp but smooth interfaces. In this paper, we verify through numerical tests the sharp interface limit of the phase field model which in fact leads to an internal discontinuity interface problem; finally, we show the efficiency of Isogeometric Analysis for the numerical approximation of the model by solving a benchmark problem, the so-called "rising bubble" problem. |
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55/2017 - 10/23/2017
Agosti, A.; Cattaneo, C.; Giverso, C.; Ambrosi, D.; Ciarletta, P.
A computational platform for the personalized clinical treatment of glioblastoma multiforme | Abstract | | In this work, we develop a computational tool to predict the patient-specific evolution of a highly malignant
brain tumour, the glioblastoma multiforme (GBM), and its response to therapy. A diffuse-interface mathematical
model based on mixture theory is fed by clinical neuroimaging data that provide the anatomical and microstructural
characteristics of the patient brain. The model is numerically solved using the finite element method, on the basis
of suitable numerical techniques to deal with the resulting Cahn-Hilliard type equation with degenerate mobility and
single-well potential. We report the results of simulations performed on the real geometry of a patient brain, proving
how the tumour expansion is actually dependent on the local tissue structure. We also report a sensitivity analysis
concerning the effects of the different therapeutic strategies employed in the clinical Stupp protocol. The simulated
results are in qualitative agreement with the observed evolution of GBM during growth, recurrence and response to
treatment. Taken as a proof-of-concept, these results open the way to a novel personalized approach of mathematical
tools in clinical oncology.
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52/2017 - 10/16/2017
Beretta, E.; Ratti, L.; Verani, M.
A phase-field approach for the interface reconstruction in a nonlinear elliptic problem arising from cardiac electrophysiology | Abstract | | In this work we tackle the reconstruction of discontinuous coefficients in a semilinear elliptic equation from the knowledge of the solution on the boundary of the domain, an inverse problem motivated by biological application in cardiac electrophysiology.
We formulate a constraint minimization problem involving a quadratic mismatch functional enhanced with a regularization term which penalizes the perimeter of the inclusion to be identified. We introduce a phase-field relaxation of the problem, replacing the perimeter term with a Ginzburg-Landau-type energy. We prove the Gamma-convergence of the relaxed functional to the original one (which implies the convergence of the minimizers), we compute the optimality conditions of the phase-field problem and define a reconstruction algorithm based on the use of the Frechet derivative of the functional. After introducing a discrete version of the problem we implement an iterative algorithm and prove convergence properties. Several numerical results are reported, assessing the effectiveness and the robustness of the algorithm in identifying arbitrarily-shaped inclusions.
Finally, we compare our approach to a shape derivative based technique, both from a theoretical point of view (computing the sharp interface limit of the optimality conditions) and from a numerical one. |
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