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We propose and numerically assess three segregated ( partitioned) algorithms for the numerical solution of the coupled electromechanics problem for the left human ventricle. We split the coupled problem into its core mathematical models and we proceed to t ...
We consider the numerical approximation of lipid biomembranes at equilibrium described by the Canham-Helfrich model, according to which the bending energy is minimized under area and volume constraints. Energy minimization is performed via L-2-gradient flo ...
In this thesis, a computational approach is used to study two-phase flow including phase change by direct numerical simulation.
This approach follows the interface with an adaptive moving mesh.
The incompressible Navier-Stokes equations are solved, in tw ...
For two-dimensional (2D) time fractional diffusion equations, we construct a numerical method based on a local discontinuous Galerkin (LDG) method in space and a finite difference scheme in time. We investigate the numerical stability and convergence of th ...
Discretization methods such as finite differences or finite elements were usually employed to provide high fidelity solution approximations for reduced order modeling of parameterized partial differential equations. In this paper, a novel discretization te ...
Understanding the plasma dynamics in tokamaks is of fundamental importance to reliably predict the performances of future fusion devices. Because of the complex phenomena at play, state-of-the-art simulation codes are needed to investigate the plasma dynam ...
We consider the numerical approximation of lipid biomembranes, including red blood cells, described through the Canham-Helfrich model, according to which the shape minimizes the bending energy under area and volume constraints. Energy minimization is perfo ...
In this thesis, we consider the numerical approximation of high order geometric Partial Differential Equations (PDEs). We first consider high order PDEs defined on surfaces in the 3D space that are represented by single-patch tensor product NURBS. Then, we ...
This paper is devoted to determining a space-dependent source term in an inverse problem of the time-fractional diffusion equation. We use a fully-discrete method based on a finite difference scheme in time and a local discontinuous Galerkin method (LDG) i ...
This article presents a geometric approach to some similarity problems involving metric arguments in the non-positively curved space of positive invertible operators of an operator algebra and the canonical isometric action by invertible elements on the co ...
