Related papers: High-order exponential solver method for particle-…
Next-generation high-power lasers that can be focused to intensities exceeding 10^23 W/cm^2 are enabling new physics and applications. The physics of how these lasers interact with matter is highly nonlinear, relativistic, and can involve…
The finite-difference time-domain (FDTD) method is a well established method for solving the time evolution of Maxwell's equations. Unfortunately the scheme introduces numerical dispersion and therefore phase and group velocities which…
A high fidelity flow simulation for complex geometries for high Reynolds number ($Re$) flow is still very challenging, which requires more powerful computational capability of HPC system. However, the development of HPC with traditional CPU…
The development of ultra-intense laser-based sources of high energy ions is an important goal, with a variety of potential applications. One of the barriers to achieving this goal is the need to maximize the conversion efficiency from laser…
We present a mimetic finite-difference approach for solving Maxwell's equations in one and two spatial dimensions. After introducing the governing equations and the classical Finite-Difference Time-Domain (FDTD) method, we describe mimetic…
In this work, the fast-convolving reproducing kernel particle method (FC-RKPM) is introduced. This method is hundreds to millions of times faster than the traditional RKPM for 3D meshfree simulations. In this approach, the meshfree…
This paper discusses a novel fully implicit formulation for a 1D electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov-Poisson…
Many current laser wakefield acceleration (LWFA) experiments are carried out in a regime where the laser pulse length is on the order of or longer than the wake wavelength and where ionization injection is employed to inject electrons into…
In this paper, we present a novel numerical framework for solving a specific biological reaction-diffusion-advection system of cancer growth in three dimensions (3D) using particles of variable mass. We adopt empirical particle measures to…
Kinetic plasma simulations solve the Vlasov-Poisson or Vlasov-Maxwell equations to evolve scalar-variable distribution functions in position-velocity phase space and vector-variable electromagnetic fields in physical space. The…
We consider the numerical solution of partial differential equations with coefficients that are strongly heterogeneous in space. We provide an overview of higher-order localized orthogonal decomposition (LOD) methods for the elliptic…
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast…
For many plasma physics problems, three-dimensional and kinetic effects are very important. However, such simulations are very computationally intensive. Fortunately, there is a class of problems for which there is nearly azimuthal symmetry…
The quality of electron bunches accelerated by laser wakefields is highly dependant on the temporal and spatial features of the laser driver. Analysis of experiments performed at APOLLON PW-class laser facility shows that spatial…
Elliptic interface problems whose solutions are $C^0$ continuous have been well studied over the past two decades. The well-known numerical methods include the strongly stable generalized finite element method (SGFEM) and immersed FEM…
We propose a finite difference method to solve Maxwell's equations in time domain in the presence of a perfect electric conductor that impedes the propagations of electromagnetic waves. Our method is a modification of the existing approach…
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…
For decades, the Vlasov-Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency.…
A more accurate, stable, finite-difference time-domain (FDTD) algorithm is developed for simulating Maxwell's equations with isotropic or anisotropic dielectric materials. This algorithm is in many cases more accurate than previous…
In this paper, we introduce a new finite expression method (FEX) to solve high-dimensional partial integro-differential equations (PIDEs). This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel…