相关论文: NRPyElliptic: A Fast Hyperbolic Relaxation Ellipti…

In this paper, we propose a novel shape optimization approach for the source identification of elliptic equations. This identification problem arises from two application backgrounds: actuator placement in PDE-constrained optimal controls…

We develop a boundary integral equation solver for elliptic partial differential equations on complex \threed geometries. Our method is efficient, high-order accurate and robustly handles complex geometries. A key component is our singular…

In a recent MNRAS article, Raposo-Pulido and Pelaez (RPP) designed a scheme for obtaining very close seeds for solving the elliptic Kepler Equation with the classical and the modified Newton-Rapshon methods. This implied an important…

Numerical relativity has traditionally been pursued via finite differencing. Here we explore pseudospectral collocation (PSC) as an alternative to finite differencing, focusing particularly on the solution of the Hamiltonian constraint (an…

Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts, including solution of partial differential equations (PDEs). We describe a solver for multiscale fully nonlinear elliptic…

In numerical evolutions of binary black holes (BBH) it is desirable to easily control the orbital eccentricity of the BBH, and the number of orbits completed by the binary through merger. This paper presents fitting formulae that allow to…

We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…

Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availability of high-performance computing infrastructure, many…

We present a novel spectral solver for general relativistic magnetohydrodynamics on dynamical spacetimes. By combining a high order discontinuous spectral method on mapped Chebyshev Fourier grids, our scheme attains exponential convergence.…

The focus of this work is on the construction of initial data including a neutron star on a hyperboloidal slice. As simplest scenario for this first step, spherical symmetry is considered together with a polytropic-like equation of state…

We present a computational framework (Rio) in the ADM 3+1 approach for numerical relativity. This work enables us to carry out high resolution calculations for initial data of two arbitrary black holes. We use the transverse conformal…

We present a new iterative method to reduce eccentricity in black-hole-binary simulations. Given a good first estimate of low-eccentricity starting momenta, we evolve puncture initial data for ~4 orbits and construct improved initial…

Approximate solutions to the Einstein field equations are a valuable tool to investigate gravitational phenomena. An important aspect of any approximation is to investigate and quantify its regime of validity. We present a study that…

An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to…

To improve the spatial resolution of power Doppler (PD) imaging, we explored null subtraction imaging (NSI) as an alternative beamforming technique to delay-and-sum (DAS). NSI is a nonlinear beamforming approach that uses three different…

A new algorithm, denoted by RSRR, is presented for solving large-scale nonlinear eigenvalue problems (NEPs) with a focus on improving the robustness and reliability of the solution, which is a challenging task in computational science and…

An elliptic relative equilibrium (ERE) is a special solution of the planar $N$-body problem generated by a central configuration. Its linear stability depends on the eccentricity $e$ and the masses of the bodies. However, for $e>0$, the…

There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…

The aim of this work is to prove existence and uniqueness results for a doubly nonlinear elliptic problem that is essential for solving the associated parabolic problem using Rothe's method (discretizing time). We work under very weak…

This work extends the paradigm of evolutional deep neural networks (EDNNs) to solving parametric time-dependent partial differential equations (PDEs) on domains with geometric structure. By introducing positional embeddings based on…