1,721,468 research outputs found
8 Reduced-order modeling for applications to the cardiovascular system
No full textThe capability to provide fast and reliable numerical simulations is of paramount importance when dealing with complex applications arising from medicine. More than for other branches of engineering and applied sciences, performing accurate computations in a short amount of time - minutes, rather than hours, or even days - is crucial when dealing with problems arising from life sciences, like, e. g., in the simulation of the cardiovascular system. Moreover, many sources of variability carried by subject-specific features have to be incorporated into the mathematical models, to quantify their impact on the computed results. For these reasons, bringing computational results into clinical practice represents a great challenge. Reducedorder modeling techniques such as the reduced basis method represent a key tool towards the possibility to address these challenges, thus making the numerical modeling of the cardiovascular system a new, fascinating testbed for these methodologies
Spectral methods for singular perturbation problems
Full text linksummary:We study spectral discretizations for singular perturbation problems. A special technique of stabilization for the spectral method is proposed. Boundary layer problems are accurately solved by a domain decomposition method. An effective iterative method for the solution of spectral systems is proposed. Suitable components for a multigrid method are presented
Some evaluations of the fractional p-Laplace operator on radial functions
Full text linkWe face a rigidity problem for the fractional -Laplace operator to extend to this new framework some tools useful for the linear case. It is known that and are constant functions in for fixed and . We evaluated proving that it is not constant in for some and . This conclusion is obtained numerically thanks to the use of very accurate Gaussian numerical quadrature formulas
Approximation of free-surface flows by biuniqueness models
No full textDottorato di ricerca in matematica computazionale e ricerca operativa. Supervisors Alfio Quarteroni e Fausto SaleriConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7 Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal
Basic ideas and tools for projection-based model reduction of parametric partial differential equations
Full text linkWe provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions, offline-online decomposition and error estimation is introduced. Several tools for geometry parametrizations, such as free form deformation, radial basis function interpolation and inverse distance weighting interpolation are explained. The empirical interpolation method is introduced as a general tool to deal with non-affine parameter dependency and non-linear problems. The discrete and matrix versions of the empirical interpolation are considered as well. Active subspaces properties are discussed to reduce high-dimensional parameter spaces as a pre-processing step. Several examples illustrate the methodologies
The non-circular shape of FloWatch(r)-PAB prevents the need for pulmonary artery reconstruction after banding. Computational fluid dynamics and clinical correlations
No full textTowards a patient-specific stroke risk assessment in atrial fibrillation using computational fluid dynamics
No full textModel Order Reduction. Volume 3: Applications
Full text linkAn increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science
Model Order Reduction. Volume 2: Snapshot-Based Methods and Algorithms
Full text linkAn increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science
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