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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59/2021 - 09/27/2021
Stella, S.; Regazzoni, F.; Vergara, C.; Dede', L.; Quarteroni, A.
A fast cardiac electromechanics model coupling the Eikonal and the nonlinear mechanics equations | Abstract | | We present a new model of human cardiac electromechanics for the left ventricle where electrophysiology is described by a Reaction-Eikonal model and which enables an off-line resolution of the reaction model, thus entailing a big saving of computational time. Subcellular dynamics is coupled with a model of tissue mechanics, which is in turn coupled with a windkessel model for blood circulation. Our numerical results show that the proposed model is able to provide a physiological response to changes in certain variables (end-diastolic volume, total peripheral resistance, contractility). We also show that our model is able to reproduce with high accuracy (and with a considerably lower computational time) the results that we would obtain if the monodomain model should be used in place of the Eikonal model. |
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58/2021 - 08/25/2021
Tassi, T., Zingaro, A., Dede', L.
Enhancing numerical stabilization methods for advection dominated differential problems by Machine Learning algorithms | Abstract | | In this work, we propose a residual-based stabilization method for advection dominated differential problems enhanced by artificial neural networks. Specifically, we consider the Streamline Upwind Petrov-Galerkin stabilization method and we employ neural networks to compute an optimal form of the stabilization parameter on which the method relies. We train the neural network on a dataset generated by repeatedly solving an optimization problem, by minimizing the distance between the numerical solution and the exact one for different parametrizations of problem data and setting of the numerical scheme. The trained network is later used to predict the optimal stabilization for any given configuration and to be readily used ``online" for any new configuration of the problem. 1D and 2D numerical tests show that our novel approach leads to more accurate solutions than the standard approaches for the problem under consideration. |
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57/2021 - 08/24/2021
Roberto Piersanti, Francesco Regazzoni, Matteo Salvador, Antonio F. Corno, Luca Dede', Christian Vergara, Alfio Quarteroni
3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics | Abstract | | Two crucial factors for accurate numerical simulations of cardiac electromechanics, which are also essential to reproduce the synchronous activity of the heart, are: i) accounting for the interaction between the heart and the circulatory system that determines pressures and volumes loads in the heart chambers; ii) reconstructing the muscular fiber architecture that drives the electrophysiology signal and the myocardium contraction. In this work, we present a 3D biventricular electromechanical model coupled with a 0D closed-loop model of the whole cardiovascular system that addresses the two former crucial factors. With this aim, we introduce a boundary condition for the mechanical problem that accounts for the neglected part of the domain located on top of the biventricular basal plane and that is consistent with the principles of momentum and energy conservation. We also discuss in detail the coupling conditions that stand behind the 3D and the 0D models. We perform electromechanical simulations in physiological conditions using the 3D-0D model and we show that our results match the experimental data of relevant mechanical biomarkers available in literature. Furthermore, we investigate different arrangements in cross-fibers active contraction. We prove that an active tension along the sheet direction counteracts the myofiber contraction, while the one along the sheet-normal direction enhances the cardiac work. Finally, several myofiber architectures are analysed. We show that a different fiber field in the septal area and in the transmural wall effect the pumping functionality of the left ventricle. |
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56/2021 - 08/24/2021
Zingaro, A.; Fumagalli, I.; Dede' L.; Fedele M.; Africa P.C.; Corno A.F.; Quarteroni A.
A multiscale CFD model of blood flow in the human left heart coupled with a lumped parameter model of the cardiovascular system | Abstract | | In this paper, we present a novel computational model for the numerical simulation of blood flow in the human heart by focusing on 3D CFD of the left heart. With the aim of simulating the hemodynamics of the left heart, we employ the Navier-Stokes equations in an Arbitrary Lagrangian Eulerian formulation to account for the endocardium motion and we model both mitral and aortic valves by means of the Resistive Immersed Implicit Surface method. To enhance the physiological significance of our numerical simulations, we use a 3D cardiac electromechanical model of the left ventricle coupled to a lumped parameter closed-loop
model of the circulation and the remaining cardiac chambers. To extend the left ventricle motion to the endocardium of the whole left heart, we introduce a preprocessing procedure that combines the harmonic extension of the left ventricle displacement and a volume-based motion of the left atrium. We thus obtain a coupled one-way electromechanical - fluid dynamics model. To better match the 3D CFD with blood circulation, we also couple the 3D Navier-Stokes equations - with motion driven by electromechanics - to the 0D circulation model. We obtain a multiscale coupled 3D-0D fluid dynamics model that we solve through a partitioned numerical scheme. We carry out numerical simulations on a healthy left heart and we validate our model by showing that some hemodynamic indicators are correctly reproduced. We finally show that our model is able to simulate the left heart's blood flow in the scenario of a regurgitant mitral valve. |
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55/2021 - 08/03/2021
Buchwald, S.; Ciaramella, G.; Salomon, J.
ANALYSIS OF A GREEDY RECONSTRUCTION ALGORITHM | Abstract | | A novel and detailed convergence analysis is presented for a greedy algorithm that
was introduced in 2009 by Maday and Salomin for operator reconstruction problems in the field of quantum mechanics.
This algorithm is based on an offline/online decomposition of the reconstruction process and on
an ansatz for the unknown operator obtained by an a priori chosen set of linearly independent
matrices. The presented convergence analysis focuses on linear-quadratic (optimization) problems
governed by linear differential systems and reveals the strong dependence of the performance of
the greedy algorithm on the observability properties of the system and on the ansatz of the basis
elements. Moreover, the analysis allows us to use a precise (and in some sense optimal) choice of
basis elements for the linear case and led to the introduction of a new and more robust optimized
greedy reconstruction algorithm. This optimized approach also applies to nonlinear Hamiltonian
reconstruction problems, and its efficiency is demonstrated by numerical experiments. |
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54/2021 - 08/03/2021
Ciaramella, G.; Gander, M.J.; Mamooler, P.
HOW TO BEST CHOOSE THE OUTER COARSE MESH IN THE DOMAIN DECOMPOSITION METHOD OF BANK AND JIMACK | Abstract | | In a previous work, we defined a new partition of unity for the Bank-Jimack domain decomposition method in
1D and proved that with the new partition of unity, the Bank-Jimack method is an optimal Schwarz method in
1D and thus converges in two iterations for two subdomains: it becomes a direct solver, and this independently
of the outer coarse mesh one uses! In this paper, we show that the Bank-Jimack method in 2D is an optimized
Schwarz method and its convergence behavior depends on the structure of the outer coarse mesh each subdomain
is using. For an equally spaced coarse mesh its convergence behavior is not as good as the convergence behavior of
optimized Schwarz. However, if a stretched coarse mesh is used, then the Bank-Jimack method becomes faster then
optimized Schwarz with Robin or Ventcell transmission conditions. Our analysis leads to a conjecture stating that
the convergence factor of the Bank-Jimack method with overlap L and m geometrically stretched outer coarse mesh
cells is $1 ? O(L^{1/2m})$. |
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53/2021 - 08/03/2021
Ciaramella, G.; Mechelli, L.
On the effect of boundary conditions on the scalability of Schwarz methods | Abstract | | In contrast with classical Schwarz theory, recent results have shown that for special domain geometries,
one-level Schwarz methods can be scalable. This property has been proved for the Laplace equation and external
Dirichlet boundary conditions. Much less is known if mixed boundary conditions are considered.
This short manuscript focuses on the convergence and scalability analysis of one-level parallel Schwarz method
and optimized Schwarz method for several different external configurations of boundary conditions, i.e.,
mixed Dirichlet, Neumann and Robin conditions. |
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52/2021 - 08/03/2021
Ciaramella, G.; Mechelli, L.
An overlapping waveform-relaxation preconditioner for economic optimal control problems with state constraints | Abstract | | In this work, a class of parabolic economic optimal control problems is considered.
These problems are characterized by pointwise state constraints regularized by a parameter,
which transforms the pure state constraints in mixed control-state ones.
However, the convergence of classical (semismooth) Newton methods deteriorates
for decreasing values of the regularization parameter. To tackle this problem, a nonlinear
preconditioner is introduced. This is based on an overlapping optimized waveform-relaxation method
characterized by Robin transmission conditions. Numerical experiments show that appropriate
choices of the overlap and of the Robin parameter lead to a preconditioned Newton method with a robust convergence
against the state constraints regularization parameter. |
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