A two-component Matched Interface and Boundary (MIB) regularization for charge singularity in implicit solvation
We present a new Matched Interface and Boundary (MIB) regularization method for treating charge singularity in solvated biomolecules whose electrostatics are described by the PoissonBoltzmann (PB) equation. In a regularization method, by decomposing the ...
A structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives
In this manuscript, we consider an initial-boundary-value problem governed by a (1+1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model ...
A numerical method for predicting Rayleigh surface wave velocity in anisotropic crystals
A numerical method was developed for calculating the Rayleigh Surface Wave (RSW) velocity in arbitrarily oriented single crystals in 360 degrees of propagation. This method relies on the results from modern analysis of RSW behavior with the Stroh ...
An asynchronous spacetime discontinuous Galerkin finite element method for time domain electromagnetics
We present an asynchronous spacetime discontinuous Galerkin (aSDG) method for time domain electromagnetics in which space and time are directly discretized. By using differential forms we express Maxwell's equations and consequently their discontinuous ...
Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients
We present a novel approach for solving steady-state stochastic partial differential equations in high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis ...
An energy-conserving method for stochastic Maxwell equations with multiplicative noise
In this paper, it is shown that three-dimensional stochastic Maxwell equations with multiplicative noise are stochastic Hamiltonian partial differential equations possessing a geometric structure (i.e. stochastic multi-symplectic conservation law), and ...
Block-diagonalization of the variational nodal response matrix using the symmetry group theory
To further improve the efficiency of the Variational Nodal Method (VNM) for solving the neutron transport equation in hexagonal-z geometry, the nodal response matrix is further block-diagonalized by utilizing the symmetry group theory to decompose the ...
Estimation of curvature from volume fractions using parabolic reconstruction on two-dimensional unstructured meshes
This paper proposes a method to estimate the curvature of an interface represented implicitly by discrete volume fractions on an unstructured two-dimensional mesh. The method relies on the computation of local parabolic reconstructions of the interface. ...
Kinetic simulation technique for plasma flow in strong external magnetic field
A technique for the kinetic simulation of plasma flow in strong external magnetic fields was developed which captures the compression and expansion of plasma bound to a magnetic flux tube as well as forces on magnetized particles within the flux tube. ...
An adaptive reconstruction for Lagrangian, direct-forcing, immersed-boundary methods
Lagrangian, direct-forcing, immersed boundary (IB) methods have been receiving increased attention due to their robustness in complex fluid-structure interaction problems. They are very sensitive, however, on the selection of the Lagrangian grid, which ...
Topology optimization of hyperelastic structures using a level set method
Soft rubberlike materials, due to their inherent compliance, are finding widespread implementation in a variety of applications ranging from assistive wearable technologies to soft material robots. Structural design of such soft and rubbery materials ...
A multidimensional unified gas-kinetic scheme for radiative transfer equations on unstructured mesh
In order to extend the unified gas kinetic scheme (UGKS) to solve radiative transfer equations in a complex geometry, a multidimensional asymptotic preserving implicit method on unstructured mesh is constructed in this paper. With an implicit ...
A multigrid AMR algorithm for the study of magnetic reconnection
We address the study of reconnecting instabilities in magnetized plasmas, a highly multiscale process, using an innovative adaptive scheme based on Adaptive Mesh Refinement (AMR) and Multigrid Algorithms. The reduced model we exploit is very sensitive ...