Related papers: New Phase-Integral Method Platform Function

A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…

Interior Point Methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task of an interior point iteration. If, due…

High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…

Astronomical optical interferometers sample the Fourier transform of the intensity distribution of a source at the observation wavelength. Because of rapid perturbations caused by atmospheric turbulence, the phases of the complex Fourier…

In recent years, the immersed finite element methods (IFEM) introduced in \cite{Li2003}, \cite{Li2004} to solve elliptic problems having an interface in the domain due to the discontinuity of coefficients are getting more attentions of…

We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…

We propose the Compact Coupling Interface Method (CCIM), a finite difference method capable of obtaining second-order accurate approximations of not only solution values but their gradients, for elliptic complex interface problems with…

In recent years, with the advancements in machine learning and neural networks, algorithms using physics-informed neural networks (PINNs) to solve PDEs have gained widespread applications. While these algorithms are well-suited for a wide…

This paper proposes a novel higher-order multi-scale (HOMS) computational method, which is highly targeted for efficient, high-accuracy and low-computational-cost simulation of hygro-thermo-mechanical (H-T-M) coupling problems in…

Symmetric informationally complete measurements are both important building blocks in many quantum information protocols and the seminal example of a generalised, non-orthogonal, quantum measurement. In higher-dimensional systems, these…

Integrated photonic devices have become pivotal elements across most research fields that involve light-based applications. A particularly versatile category of this technology are programmable photonic integrated processors, which are…

This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the…

We use a semi-numerical method to find the position and period of periodic orbits in a bisymmetrical potential, made up of a two dimensional harmonic oscillator, with an additional term of a Plummer potential, in a number of resonant cases.…

The current ghost imaging phase reconstruction schemes require either complex optical systems, Fourier transform steps, or iterative algorithms, which may increase the difficulty of system design, cause phase retrieval error or take too…

Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…

Reconfigurable intelligent surfaces (RISs) are often assumed to allow continuous phase control over all elements, leading to hardware cost that scales with the number of elements. Treating the phase of each element as a discrete variable is…

This paper surveys recent numerical advances in the phase field method for geometric surface evolution and related geometric nonlinear partial differential equations (PDEs). Instead of describing technical details of various numerical…

With the path integral approach, the thermal average in a multi-electronic-state quantum systems can be approximated by the ring polymer representation on an extended configuration space, where the additional degrees of freedom are…

The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…

This study employed an artificial intelligence-enhanced molecular simulation framework to enable efficient Path Integral Molecular Dynamics (PIMD) simulations. Owing to its modular architecture and high-throughput capabilities, the…