Related papers: Nonuniform 3D finite difference elastic wave simul…
A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…
A novel 3-D higher-order finite-difference time-domain framework with complex frequency-shifted perfectly matched layer for the modeling of wave propagation in cold plasma is presented. Second- and fourth-order spatial approximations are…
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the…
The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one…
We present the derivation, implementation, and analysis of a multiresolution adaptive grid framework for numerical simulations on octree-based 3D block-structured collocated grids with distributed computational architectures. Our approach…
Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…
Most of numerical methods for deterministic simulations of rarefied gas flows use the discrete velocity (or discrete ordinate) approximation. In this approach, the kinetic equation is approximated with a global velocity grid. The grid must…
Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In multi-dimensions, where the…
This paper presents a high-order discontinuous Galerkin (DG) scheme for the simulation of wave propagation through coupled elastic-acoustic media. We use a first-order stress-velocity formulation, and derive a simple upwind-like numerical…
Efficient and accurate numerical simulation of seismic wave propagation is important in various Geophysical applications such as seismic full waveform inversion (FWI) problem. However, due to the large size of the physical domain and…
We establish a new framework for image registration, which is based on linear elasticity and optimal mass transportation theory. We combine these two arguments in order to obtain a PDE constrained optimization problem that is analytically…
The life-cycle of a partial differential equation (PDE) solver is often characterized by three development phases: the development of a stable numerical discretization, development of a correct (verified) implementation, and the…
In this paper, we investigate the use of a mass lumped fully explicit time stepping scheme for the discretisation of the wave equation with underlying material parameters that vary at arbitrarily fine scales. We combine the leapfrog scheme…
In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…
A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear…
Here we present first results simulating plasma filaments in non-axisymmetric geometries, using a fluid turbulence extension of the \boutxx~framework. This is made possible by the implementation of the Flux Coordinate Independent scheme for…
In this paper anisotropic and dispersive wave propagation within linear strain-gradient elasticity is investigated. This analysis reveals significant features of this extended theory of continuum elasticity. First, and contrarily to…
This paper presents novel methodologies for the numerical simulation of scattering of elastic waves by both closed and open surfaces in three-dimensional space. The proposed approach utilizes new integral formulations as well as an…
We introduce a new finite element (FE) discretization framework applicable for covariant split equations. The introduction of additional differential forms (DF) that form pairs with the original ones permits the splitting of the equations…
In this paper, we propose an approach for describing wave propagation in finite-size microstructured metamaterials using a reduced relaxed micromorphic model. This method introduces an additional kinematic field with respect to the…