Related papers: Adaptive spectral solution method for the Landau a…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
Energetic electrons are of interest in many types of plasmas, however previous modeling of their properties has been restricted to the use of linear Fokker-Planck collision operators or non-relativistic formulations. Here, we describe a…
We present the design and implementation of an L2-stable spectral method for the discretization of the Vlasov- Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov…
The micromagnetic Fokker-Planck equation is solved for a uniaxial particle in the low-temperature limit. Asymptotic series in the parameter that is the inverse barrier height-to-temperature ratio are derived. With the aid of these series,…
In the present paper the linearized problem of half-space plasma oscillations in external longitudinal alternating electric field is solved analytically. Specular - accommodative boundary conditions of electron reflection from the plasma…
We present an ab initio approach to solve the time-dependent Schr\"odinger equation to treat electron and photon impact multiple ionization of atoms or molecules. It combines the already known time scaled coordinate method with a new high…
Simulation of unsteady creeping flows in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. To reduce the cost and allow for computations at much larger scales, we…
An implicit and conservative numerical scheme is proposed for the isotropic quantum Fokker-Planck equation describing the evolution of degenerate electrons subject to elastic collisions with other electrons and ions. The electron-ion and…
Recently, several works have shown that natural modifications of the classical conditional gradient method (aka Frank-Wolfe algorithm) for constrained convex optimization, provably converge with a linear rate when: i) the feasible set is a…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
A new integration scheme, combining the stability and the precision of usual pseudo-spectral codes with the locality of finite differences methods, is introduced. It turns out to be particularly suitable for the study of front and…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
We apply polynomial approximation methods -- known in the numerical PDEs context as spectral methods -- to approximate the vector-valued function that satisfies a linear system of equations where the matrix and the right hand side depend on…
The study of parametric differential equations plays a crucial role in weather forecasting and epidemiological modeling. These phenomena are better represented using fractional derivatives due to their inherent memory or hereditary effects.…
This paper presents a p-adaptive high-order hybridizable discontinuous Galerkin spectral element method (HDG-SEM) for solving the Poisson equation in electrostatic plasma simulations using particle-in-cell (PIC) schemes. This approach…
Numerically solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive refinement algorithms, in particular when functional…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…
Several challenging problem in clustering, partitioning and imaging have traditionally been solved using the "spectral technique". These problems include the normalized cut problem, the graph expander ratio problem, the Cheeger constant…
Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…
We introduce a new method with spectral accuracy to solve linear non-autonomous ordinary differential equations (ODEs) of the kind $ \frac{d}{dt}\tilde{u}(t) = \tilde{f}(t) \tilde{u}(t)$, $\tilde{u}(-1)=1$, with $\tilde{f}(t)$ an analytic…