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 1238 products
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MOX 58 - 04/26/2005
Deparis, Simone; Discacciati, Marco; Fourestey, Gilles; Quarteroni, Alfio
Fluid-structure algorithms based on Steklov-Poincaré operators | Abstract | | In this paper we review some classical algorithms for fluid structure interaction problems and we propose an alternative viewpoint mutuated from the domain decomposition theory. This approach yields preconditioned Richardson iterations on the Steklov-Poincaré nonlinear equation at the fluid-structure interface |
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MOX 57 - 04/19/2005
Di Pietro, Daniele A.; Veneziani, Alessandro
Expression Templates Implementation of Continuous and Discontinous Galerkin Methods | Abstract | | Efficiency and flexibility are often mutually exclusive features in a code. This still prompts a large part of the Scientific Computing Community to use traditional procedural language. In the last years, however, new programming techniques have been introduced allowing for a high level of abstraction without loss of performance. In this paper we present an application of the Expression Templates technique introduced in [13] to the assembly step of a finite element computation. We show that a suitable implementation, such that the compiler has the role of parsing abstract operations, allows for user-friendliness and gain in performance with respect to more traditional techniques. Both the cases of confonforming and discontinuous Galerkin finite element discretization are considered. The proposed implementation is finally applied to a number of problems entailing different kind of complications. |
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MOX 56 - 03/24/2005
Martin, Vincent; Clément, F.; Decoene, A.; Gerbeau, J.F.
Parameter identification for a one-dimensional blood flow model | Abstract | | The purpose of this work is to use a variational method to identify some of the parameters of one-dimensional models for blood flow in arteries. These parameters can be fit to approach as much as possible some data coming from experimental measurements or from numerical simulations performed using more complex models.
A nonlinear least squares approach to parameter estimation was taken, based on the optimization of a cost function. The resolution of such an optimization problem generally requires the efficient and accurate computation of the gradient of the cost function with respect to the parameters. This gradient is computed analytically when the one-dimensional hyperbolic model is discretized with a second order Taylor-Galerkin scheme. An adjoint approach, involving the resolution of an adjoint problem, was used.
Some preliminary numerical tests are shown. In these simulation, we mainly focused on detrmining a parameter that is linked to the mechanical properties of the arterial walls, the compliance. The synthetic data we used to estimated the parameter were obtained from a numerical computation performed with a more precise model: a three-dimensional fluid structure interaction model. The first results seem to be promising. In particular, it is woth noticing that the estimated compliance which gives the best fit is qiute different from the values one would have expected a priori. |
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MOX55 - 02/18/2005
Dede', L.; Quarteroni, A.
Optimal Control and Numerical Adaptivity for Advection-Diffusion Equations | Abstract | | We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection-diffusion equation, based on a stabilization method applied to the Lagrangian functional, rather than stabilizing the state and adjoint equation separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from splitting the error on the cost functional into the sum of an iteration error plus a discretization error. Once the former is reduced below a given threshold (and therefore the computed solution is near the optimal solution), the adaptive strategy is operated on the discretization error. To prove the effectiveness of the proposed methods, we report some numerical tests, referring to problems in which the control term is the source term of the advection-diffusion equation. |
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MOXP4 - 02/12/2005
Veneziani, Alessandro; Foa, Erika
Simulazione Numerica di Pompe per Macchine Lavatrici
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MOX 54 - 01/21/2005
Agoshkov, Valery; Quarteroni, Alfio; Rozza, Gianluigi
A Mathematical Approach in the Design of Arterial Bypass Using Unsteady Stokes Equations | Abstract | | In this paper we present an approach for the study of Aorto-Coronaric bypass anastomoses configurations using unsteady Stokes equations. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the incoming branch of the bypass (the toe) into the coronary according to several optimality criteria. |
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MOX 53 - 01/10/2005
Formaggia, Luca; Quarteroni, Alfio; Veneziani, Alessandro
The circulatory system: from case studies to mathematical modeling
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MOX 52 - 11/25/2004
Bottasso, Carlo L.; Maisano, Giorgio; Micheletti, Stefano; Perotto, Simona
New recovery based a posteriori error estimators | Abstract | | In this paper we formulate some new a posteriori recovery-based error estimators. The first one provides us with an improved approximation for the solution gradient. The other two furnish and estimate for the $L^2$-norm of the error on the solution itself. In more detail, the first estimator is a variant of the well-known Zienckiewicz-Zhu method and it turns out to be exact 1D for quadratic solution on non-uniform grids. The second one is based on a solution enrichment relying upon the Zienckiewicz-zhu recovered gradient. Finally the third estimator consists of a roughening of the solution followed by a Zienckiewicz-Zhu-like recovery applied to the solution itself. The three new proposed methods are compared in terms of their effectivity indices and solution accuracy on two and three dimensional problems |
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