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 1287 products
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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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51/2021 - 08/03/2021
Ciaramella, G.; Kwok, F.; Mueller, G.
Nonlinear optimized Schwarz preconditioner for elliptic optimal control problems | Abstract | | We introduce a domain decomposition-based nonlinear preconditioned iteration for solving nonlinear, nonsmooth elliptic optimal control problems, with a nonlinear reaction term, $L^1$ regularization and box constraints on the control function. The method is obtained by applying semismooth Newton to the fixed-point equation of the parallel optimized Schwarz iteration. As a proof of concept, numerical experiments are performed on two subdomains, as well as on a multi-subdomain test case. The results show that it is possible to obtain substantial improvements in robustness and efficiency with the
new method, relative to semismooth Newton applied directly to the full optimization problem, provided appropriate Robin parameters and a good continuation strategy are chosen. |
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50/2021 - 08/03/2021
Ciaramella, G.; Vanzan, T.
On the asymptotic optimality of spectral coarse spaces | Abstract | | This paper is concerned with the asymptotic optimality of
spectral coarse spaces for two-level iterative methods. Spectral coarse spaces, namely coarse spaces obtained as the span of the slowest modes of the used one-level smoother, are known to be very efficient and, in some cases, optimal.
However, the results of this paper show that spectral coarse spaces do not necessarily minimize the asymptotic contraction factor of a two-level iterative method.
Moreover, the presented numerical experiments show that there exist coarse spaces that are asymptotically more efficient and lead to preconditioned systems with improved conditioning
properties. |
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49/2021 - 07/21/2021
Rea, F.; Savaré, L; Franchi, M.; Corrao, G; Mancia, G
Adherence to Treatment by Initial Antihypertensive Mono and Combination Therapies | Abstract | | BACKGROUND
Aim of our study was to compare adherence to antihypertensive drug
therapy between newly treated patients in whom monotherapy or a
2-drug single-pill combination (SPC) was initially dispensed.
METHODS
The 63,448 residents of Lombardy Region (Italy), aged 40–80 years,
who were newly treated with antihypertensive drugs during 2016,
were identified and followed for 1 year after the first prescription. The
outcome of interest was adherence to drug therapy that was measured
according to the “proportion of days covered” (PDC) criterion, i.e.,
the ratio between the number of days in which the drug was available
and the days of follow-up. Patients who had a PDC >75% and
<25% were defined as highly and poorly adherent to drug therapy,
respectively. Log-binomial regression models were fitted to compare
the propensity to treatment adherence between the initial therapeutic
strategies, after adjusting for baseline demographic and clinical
covariates.
RESULTS
About 46% and 17% of patients showed high and poor adherence, respectively.
Compared with patients under initial monotherapy (85%),
those who were initially treated with a SPC (15%) had higher propensity
to be highly adherent and a lower propensity to be poorly adherent
to antihypertensive treatment (risk ratio: 1.18, 95% confidence interval
1.16–1.21; 0.42, 0.39–0.45, respectively). This was the case regardless the
sex, the age, the patient clinical status, and with almost any type of SPC.
CONCLUSIONS
In a real-life setting, patients who were initially prescribed a 2-drug
SPC exhibited more frequently a good adherence to antihypertensive
treatment than those starting with a single drug.
Author Laura Savarè is currently affiliated to MOX-Politecnico di Milano |
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