相关论文: Multidomain Galerkin-Collocation method: spherical…

We initiate a systematic implementation of the spectral domain decomposition technique with the Galerkin-Collocation (GC) method in situations of interest such as the spherical collapse of a scalar field in the characteristic formulation.…

We study the general dynamics of the spherically symmetric gravitational collapse of a massless scalar field. We apply the Galerkin projection method to transform a system of partial differential equations into a set of ordinary…

We present a simple domain decomposition code based on the Galerkin-Collocation method to integrate the field equations of the Bondi problem. The algorithm is stable, exhibits exponential convergence when considering the Bondi formula as an…

We present a Galerkin-Collocation domain decomposition algorithm applied to the evolution of cylindrical unpolarized gravitational waves. We show the effectiveness of the algorithm in reproducing initial data with high localized gradients…

We present a new computational framework for the Galerkin-collocation method for double domain in the context of ADM 3+1 approach in numerical relativity. This work enables us to perform high resolution calculations for initial sets of two…

We develop a numerical method suitable for gravitational collapse based on Cauchy evolution with an ingoing characteristic boundary. Unlike similar methods proposed recently (Ripley; Bieri, Garfinkle & Yau 2019/20), the numerical grid…

We compute the Hamiltonian for spherically symmetric scalar field collapse in Einstein-Gauss-Bonnet gravity in D dimensions using slicings that are regular across future horizons. We first reduce the Lagrangian to two dimensions using…

In computational relativity, critical behaviour near the black hole threshold has been studied numerically for several models in the last decade. In this paper we present a spatial Galerkin method, suitable for finding numerical solutions…

We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formulate a non-iterative domain decomposition approach. Such…

We present an algebraic method for constructing a highly effective coarse grid correction to accelerate domain decomposition. The coarse problem is constructed from the original matrix and a small set of input vectors that span a low-degree…

This paper, as the sequel to previous work, develops numerical schemes for fractional diffusion equations on a two-dimensional finite domain with triangular meshes. We adopt the nodal discontinuous Galerkin methods for the full spatial…

A novel hybrid algorithm is presented for the Boltzmann-BGK equation, in which a low-rank decomposition is applied solely in the velocity subspace, while a full-rank representation is maintained in the physical (position) space. This…

A hybridized discontinuous Galerkin method is proposed for solving 2D fractional convection-diffusion equations containing derivatives of fractional order in space on a finite domain. The Riemann-Liouville derivative is used for the spatial…

This paper constructs continuously self-similar solution of a spherically symmetric gravitational collapse of a scalar field in n dimensions. The qualitative behavior of these solutions is explained, and closed-form answers are provided…

This article considers a new discretization scheme for conservation laws. The discretization setting is based on a discontinuous Galerkin scheme in combination with an approximation space that contains high-order polynomial modes as well as…

In this work, we propose and investigate stable high-order collocation-type discretisations of the discontinuous Galerkin method on equidistant and scattered collocation points. We do so by incorporating the concept of discrete least…

We describe a formalism and numerical approach for studying spherically symmetric scalar field collapse for arbitrary spacetime dimension d and cosmological constant Lambda. The presciption uses a double null formalism, and is based on…

In (J. Comput. Phys., 417, 109577, 2020) we introduced a space-time embedded-hybridizable discontinuous Galerkin method for the solution of the incompressible Navier-Stokes equations on time-dependent domains of which the motion of the…

In this paper, we use Fourier analysis to study the superconvergence of the semi-discrete discontinuous Galerkin method for scalar linear advection equations in one spatial dimension. The error bounds and asymptotic errors are derived for…

We deal with the numerical solution of the time-dependent partial differential equations using the adaptive space-time discontinuous Galerkin (DG) method. The discretization leads to a nonlinear algebraic system at each time level, the size…