相关论文: A new computational framework for particle and spi…

Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…

Gaseous flows show a diverse set of behaviors on different characteristic scales. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between the flow-field solutions and the real physics. To study…

A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions…

The Source Galerkin Method is a new numerical technique that is being developed to solve Quantum Field Theories on the continuum. It is not based on Monte Carlo techniques and has a measure to evaluate relative errors. It promises to…

Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…

A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general…

This paper develops and analyses semi-discrete numerical method for two dimensional Vlasov-Stokes' system with periodic boundary condition. The method is based on coupling of semi-discrete discontinuous Galerkin method for the Vlasov…

This work aims to construct and analyze a discontinuous Galerkin method on polytopal grids (PolydG) to solve the pseudo-stress formulation of the unsteady Stokes problem. The pseudo-stress variable is introduced due to the growing interest…

The semi-Lagrangian discontinuous Galerkin method, coupled with a splitting approach in time, has recently been introduced for the Vlasov--Poisson equation. Since these methods are conservative, local in space, and able to limit numerical…

The Galerkin method is often employed for numerical integration of evolutionary equations, such as the Navier-Stokes equation or the magnetic induction equation. Application of the method requires solving an equation of the form $P(Av-f)=0$…

We propose a deep learning based discontinuous Galerkin method (D2GM) to solve hyperbolic equations with discontinuous solutions and random uncertainties. The main computational challenges for such problems include discontinuities of the…

We analyse a Monte Carlo particle method for the simulation of the calibrated Heston-type local stochastic volatility (H-LSV) model. The common application of a kernel estimator for a conditional expectation in the calibration condition…

In the present work, we examine and analyze an hp-version interior penalty discontinuous Galerkin finite element method for the numerical approximation of a steady fluid system on computational meshes consisting of polytopic elements on the…

In this paper we introduce and discuss numerical schemes for the approximation of kinetic equations for flocking behavior with phase transitions that incorporate uncertain quantities. This class of schemes here considered make use of a…

A proposal for an electron-beam device that can act as an efficient spin-polarization filter has been recently put forward [E. Karimi et al., Phys. Rev. Lett. 108, 044801 (2012)]. It is based on combining the recently developed diffraction…

This work considers stochastic Galerkin approximations of linear elliptic partial differential equations (PDEs) with stochastic forcing terms and stochastic diffusion coefficients, that cannot be bounded uniformly away from zero and…

As an extension of our previous work in Sun et.al (2018) [41], we develop a discontinuous Galerkin method for solving cross-diffusion systems with a formal gradient flow structure. These systems are associated with non-increasing entropy…

We present a new deterministic approach for the solution of the Boltzmann kinetic equation based on nodal discontinuous Galerkin (DG) discretizations in velocity space. In the new approach the collision operator has the form of a bilinear…

We outline two alternative schemes to perform numerical calculations in quantum field theory. In principle, both of these approaches are better suited to study phase structure than conventional Monte Carlo. The first method, Source…

We introduce a fast Fourier spectral method for the multi-species Boltzmann collision operator. The method retains the riveting properties of the single-species fast spectral method (Gamba et al. SIAM J. Sci. Comput., 39 pp. B658--B674…