Related papers: A fast, high-order solver for the Grad-Shafranov e…
We introduce a novel approach for the simultaneous optimization of plasma physics and coil engineering objectives using fixed-boundary equilibria that is computationally efficient and applicable to a broad range of vacuum and finite plasma…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…
The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability.…
Context. Magnetized plasmas characterized by shearing flows are present in many natural contexts, such as the Earth's magnetopause and the solar wind. The collisionless nature of involved plasmas requires a kinetic description. When the…
In this paper, we consider the numerical solution of highly-oscillatory Vlasov and Vlasov-Poisson equations with non-homogeneous magnetic field. Designed in the spirit of recent uniformly accurate methods, our schemes remain insensitive to…
In this paper, we propose a fast spectral-Galerkin method for solving PDEs involving integral fractional Laplacian in $\mathbb{R}^d$, which is built upon two essential components: (i) the Dunford-Taylor formulation of the fractional…
We describe an accelerated direct solver for the integral equations which model acoustic scattering from curved surfaces. Surfaces are specified via a collection of smooth parameterizations given on triangles, a setting which generalizes…
In this paper we provide sharp criteria for linear stability or instability of equilibria of collisionless plasmas in the presence of boundaries. Specifically, we consider the relativistic Vlasov-Maxwell system with specular reflection at…
We are concerned with Grad-Shafranov type equations, describing in dimension $N=2$ the equilibrium configurations of a plasma in a Tokamak. We obtain a sharp superlinear generalization of the result of Temam (1977) about the linear case,…
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from numerical approximation. To construct our…
Correlated phenomena occur in quantum materials because of the delicate interplay between internal degrees of freedom, leading to multiple symmetry-broken quantum phases. Resolving the structure of these phases is a key challenge, often…
In this short note, we present an easy to implement and fast algorithm for the computation of the steady solitary gravity wave solution of the free surface Euler equations in irrotational motion. First, the problem is reformulated in a…
We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a…
Elliptic equations play a crucial role in turbulence models for magnetic confinement fusion. Regardless of the chosen modeling approach - whether gyrokinetic, gyrofluid, or drift-fluid - the Poisson equation and Amp\`{e}re's law lead to…
Hot and tenuous plasmas are frequently far from local thermodynamic equilibrium, necessitating sophisticated methods for determining the associated plasma dielectric tensor and normal mode response. The Arbitrary Linear Plasma Solver…
We present a high order, Fourier penalty method for the Maxwell's equations in the vicinity of perfect electric conductor boundary conditions. The approach relies on extending the smooth non-periodic domain of the equations to a periodic…
An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting…
A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the…
The boundary problem about behavior (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with specular boundary conditions is analytically solved. The kinetic equation of…
A high-order convergent and robust numerical solver is constructed and used to find complex eigenwavenumbers and electromagnetic eigenfields of dielectric objects with axial symmetry. The solver is based on Fourier--Nystr\"om discretization…