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This paper deals with a new analytical model for microfluidic passive mixers. Two common approaches already exist for such a purpose. On the one hand, the resolution of the advection-diffusion-reaction equation (ADRE) is the first one and the closest to ph ...
The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative method and as a p ...
Finite elements methods (FEMs) have benefited from decades of development to solve partial differential equations (PDEs) and to simulate physical systems. In the recent years, machine learning (ML) and artificial neural networks (ANN) have shown great pote ...
This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a m ...
Two-level domain decomposition methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level preconditioner (or its corr ...
In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...
Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others.Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineeri ...
In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by ...
This paper presents neural network regression models for predicting the nonlinear static and linearized dynamic reaction forces of spiral grooved gas journal bearings. The partial differential equations (PDEs) are sampled, based on a full factorial and ran ...
Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide a fully discret ...