Related papers: Adaptive wavelet-based method for simulation of el…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep…
A conservative scheme has been formulated and verified for gyrokinetic particle simulations of electromagnetic waves and instabilities in magnetized plasmas. An electron continuity equation derived from drift kinetic equation is used to…
The subject of this work is a new stochastic Galerkin method for second-order elliptic partial differential equations with random diffusion coefficients. It combines operator compression in the stochastic variables with tree-based spline…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
The state-of-the-art linked Gaussian process offers a way to build analytical emulators for systems of computer models. We generalize the closed form expressions for the linked Gaussian process under the squared exponential kernel to a…
A fast and stable method is formulated to compute the time evolution of a wavefunction by numerically solving the time-dependent Schr{\"o}dinger equation. This method is a real space/real time evolution method implemented by several…
The simulation of charge transport in ultra-scaled electronic devices requires the knowledge of the atomic configuration and the associated potential. Such "atomistic" device simulation is most commonly handled using a tight-binding…
The high-order accurate continuous Galerkin finite element method offers attractive computational efficiency for computational fluid dynamics. A challenge is however spurious oscillations which result for convection dominated flows over…
Numerical methods for random parametric PDEs can greatly benefit from adaptive refinement schemes, in particular when functional approximations are computed as in stochastic Galerkin and stochastic collocations methods. This work is…
We present high order accurate numerical methods for the wave equation that combines efficient Hermite methods with eometrically flexible discontinuous Galerkin methods by using overset grids. Near boundaries we use thin boundary fitted…
In this article a simplified weak Galerkin finite element method is developed for the Dirichlet boundary value problem of convection-diffusion-reaction equations. The simplified weak Galerkin method utilizes only the degrees of freedom on…
We design and analyze a new adaptive stabilized finite element method. We construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that…
We introduce a discontinuous Galerkin method for the mixed formulation of the elasticity eigenproblem with reduced symmetry. The analysis of the resulting discrete eigenproblem does not fit in the standard spectral approximation framework…
In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an adaptive…
This paper presents an automated software toolchain for synthesizing hardware-implementable analog circuits that solve constrained optimization problems. The proposed toolchain supports nonlinear objective functions with linear and…
We use a concept of weak asymptotic solution for homogeneous as well as non-homogeneous fractional advection dispersion type equations. Using Legendre scaling functions as basis, a numerical method based on Galerkin approximation is…
In this paper, we propose an architecture for FPGA emulation of mixed-signal systems that achieves high accuracy at a high throughput. We represent the analog output of a block as a superposition of step responses to changes in its analog…
In this paper we present a new technique for efficiently implementing Large Eddy Simulation with the Discontin- uous Galerkin method on unstructured meshes. In particular, we will focus upon the approach to overcome the computational…
This paper is concerned with the construction, analysis and realization of a numerical method to approximate the solution of high dimensional elliptic partial differential equations. We propose a new combination of an Adaptive Wavelet…