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 1242 products
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57/2019 - 12/30/2019
Antonietti, P.F.; Bertoluzza, S.; Prada, D.; Verani M.
The Virtual Element Method for a Minimal Surface Problem | Abstract | | In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject to a prescribed boundary condition. We derive optimal error estimate and present several numerical tests assessing the validity of the theoretical results. |
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56/2019 - 12/30/2019
Antonietti, P.F.; Berrone, S.; Borio A.; D'Auria A.; Verani, M.; Weisser, S.
Anisotropic a posteriori error estimate for the Virtual Element Method | Abstract | | We derive an anisotropic a posteriori error estimate for the adaptive conforming Virtual Element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its approximation results to prove the reliability of the error indicator. We design and implement the corresponding adaptive polygonal anisotropic algorithm. Several numerical tests assess the superiority of the proposed algorithm in comparison with standard polygonal isotropic mesh refinement schemes. |
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55/2019 - 12/18/2019
Agosti, A.; Ciarletta, P.; Garcke, H.; Hinze, M.
Learning patient-specific parameters for a diffuse interface glioblastoma model from neuroimaging data | Abstract | | Parameters in mathematical models for glioblastoma multiforme (GBM) tumour growth
are highly patient specific. Here we aim to estimate parameters in a Cahn-Hilliard type
diffuse interface model in an optimised way using model order reduction (MOR) based on
proper orthogonal decomposition (POD). Based on snapshots derived from finite element
simulations for the full order model (FOM) we use POD for dimension reduction and solve
the parameter estimation for the reduced order model (ROM). Neuroimaging data are used
to define the highly inhomogeneous diffusion tensors as well as to define a target functional in
a patient specific manner. The reduced order model heavily relies on the discrete empirical
interpolation method (DEIM) which has to be appropriately adapted in order to deal with
the highly nonlinear and degenerate parabolic PDEs. A feature of the approach is that
we iterate between full order solves with new parameters to compute a POD basis function
and sensitivity based parameter estimation for the ROM problems. The algorithm is applied
using neuroimaging data for two clinical test cases and we can demonstrate that the reduced
order approach drastically decreases the computational effort. |
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54/2019 - 12/18/2019
Simona, A.; Bonaventura, L; de Falco, C.; Schoeps, S.
IsoGeometric Approximations for Electromagnetic Problems in Axisymmetric Domains | Abstract | | We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the radial and axial directions. This combination allows to blend the flexibility and
accuracy of IGA approaches with the advantages of a Fourier representation on axisymmetric domains. It also allows to reduce significantly the computational cost by decoupling of the computations required for each Fourier mode. We prove that
the discrete approximation spaces employed functional space constitute a closed and exact de Rham sequence. Numerical simulations of relevant benchmarks confirm the high order convergence and other computational advantages of the proposed
method. |
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53/2019 - 12/12/2019
Cerroni, D., Penati, M.; Porta, G.; Miglio, E.; Zunino, P.; Ruffo, P.
Multiscale modeling of glacial loading by a 3D Thermo-Hydro-Mechanical approach including erosion and isostasy | Abstract | | We present a computational framework that allows investigating the Thermo-Hydro-Mechanical response of a representative part of a sedimentary basin during a glaciation cycle. We tackle the complexity of the problem, arising by the mutual interaction among several phenomena, by means of a multi-physics, multi-scale model with respect to both space and time. Our contribution addresses both the generation of the computational grid and the algorithm for the numerical solution of the problem. In particular we present a multi-scale approach accounting for the global deformation field of the lithosphere coupled with the Thermo-Hydro-Mechanical feedback of the ice load on a representative part of the domain at a finer scale. In the fine scale model we also include the erosion possibly caused by the ice melting. This methodology allows investigating the evolution of the sedimentary basin as a response to glaciation cycle at a fine scale, taking also into account the large spatial scale movement of the lithosphere due to isostasy. The numerical experiments are based on the analysis of simple scenario, and show the emergence of effects due to the multi-physics nature of the problem that are barely captured by simpler approaches.
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52/2019 - 12/12/2019
Cerroni, D.; Radu, A. R. ; Zunino, P.
Numerical solvers for a poromechanic problem with a moving boundary | Abstract | | We study a poromechanic problem in presence of a moving boundary.
The poroelastic material is described by means of the Biot model while the moving boundary accounts for the effect of surface erosion of the material. We focus on the numerical approximation of the problem, in the framework of the finite element method. To avoid re-meshing along with the evolution of the boundary, we adopt the cut finite element approach. The main issue of this strategy consists of the ill-conditioning of the finite element matrices in presence of cut elements of small size. We show, by means of numerical experiments and theory, that this issue significantly decreases the performance of the numerical solver. For this reason, we propose a strategy that allows to overcome the ill-conditioned behavior of the discrete problem. The resulting solver is based on the fixed stress approach, used to iteratively decompose the Biot equations, combined with the ghost penalty stabilization and preconditioning applied to the pressure and displacement sub-problems respectively. |
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51/2019 - 12/10/2019
Parolini, N.; Riccobene, C.; Schenone, E.
Reduced models for liquid food packaging systems | Abstract | | Simulation tools are nowadays key elements for effective production, design and maintenance processes in various industrial applications. Thanks to the advances that have been achieved in the past three decades, accurate and efficient solvers for computational fluid dynamics and computational mechanics are routinely adopted for the design of many products and systems. However, the most accurate models accounting for the complete three-dimensional complex physics (of even multi-physics) are not always the best option to pursue, in particular in the preliminary design phase or whenever very fast evaluations are required. In this paper, we present a set of reduced numerical models that have been developed in the past few years to support the design of paperboard packaging systems. |
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50/2019 - 12/07/2019
Lusi, V.; Moore, T. L.; Laurino, F.; Coclite, A.; Perreira, R.; Rizzuti, I.; Palomba, R.; Zunino, P.; Duocastella, M.; Mizrahy, S.; Peer, D.; Decuzzi, P.
A tissue chamber chip for assessing nanoparticle mobility in the extravascular space | Abstract | | Although a plethora of nanoparticle configurations have been proposed over the past 10 years, the uniform and deep
penetration of systemically injected nanomedicines into the diseased tissue stays as a major biological barrier. Here, a
‘tissue chamber’ chip is designed and fabricated to study the extravascular transport of small molecules and
nanoparticles. The chamber comprises a collagen slab, deposited within a PDMS mold, and an 800 mm channel for the
injection of the working solution. Through fluorescent microscopy, the dynamics of molecules and nanoparticles was
estimated within the gel, under different operating conditions. Diffusion coefficients were derived from the analysis of
the particle mean square displacements (MSD). For validating the experimental apparatus and the protocol for data
analysis, the diffusion D of FITC-Dextran molecules of 4, 40 and 250 kDa was first quantified. As expected, D reduces
with the molecular weight of the Dextran molecules. The MSD-derived diffusion coefficients were in good agreement
with values derived via fluorescence recovery after photobleaching (FRAP), an alternative technique that solely applies
to small molecules. Then, the transport of six nanoparticles with similar hydrodynamic diameters (~ 200 nm) and
different surface chemistries was quantified. Surface PEGylation was confirmed to favor the diffusion of nanoparticles
within the collagen slab, whereas the surface decoration with hyaluronic acid (HA) chains reduced nanoparticle
mobility in a way proportionally to the HA molecular weight. To assess further the generality of the proposed approach,
the diffusion of the six nanoparticles was also tested in freshly excited brain tissue slices. In these ex-vivo experiments,
the diffusion coefficients were 5-orders of magnitude smaller than for the ‘tissue chamber’ chip. This was mostly
ascribed to the lack of a cellular component in the chip. However, the trends documented for PEGylated and HA-coated
nanoparticles in vitro were also confirmed ex-vivo. This work demonstrates that the ‘tissue chamber’ chip can be
employed to effectively and efficiently test the extravascular transport of nanomedicines while minimizing the use of
animals. |
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