Related papers: An adaptive interpolation scheme for molecular pot…
Layer potentials represent solutions to partial differential equations in an integral equation formulation. When numerically evaluating layer potentials at evaluation points close to the domain boundary, specialized quadrature techniques…
There are many methods for image enhancement. Image inpainting is one of them which could be used in reconstruction and restoration of scratch images or editing images by adding or removing objects. According to its application, different…
While there have been many developments in computational probes of both strongly-correlated molecular systems and machine-learning accelerated molecular dynamics, there remains a significant gap in capabilities in simulating accurate…
We present a combination of the recently developed double incremental expansion of potential energy surfaces with the well-established adaptive density-guided approach to grid construction. This unique methodology is based on the use of an…
An adaptive interpolation scheme is proposed to accurately calculate the wideband responses in electromagnetic simulations. In the proposed scheme, the sampling points are first carefully divided into several groups based on their responses…
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
In astrophysical and cosmological analyses, the increasing quality and volume of astronomical data demand efficient and precise computational tools. This work introduces a novel adaptive algorithm for automatic knots (AutoKnots) allocation…
Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
The calculation of scattering amplitudes at higher orders in perturbation theory has reached a high degree of maturity. However, their usage to produce physical predictions within Monte Carlo programs is often precluded by the slow…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
In the calculation of thermodynamic properties and three dimensional structures of macromolecules, such as proteins, it is important to have a good algorithm for computing solvent accessible surface area of macromolecules. Here we propose a…
We study local approximation properties in hierarchical spline spaces through a twofold approach. First, we design and analyze a robust adaptive refinement algorithm to construct locally graded meshes. Second, we establish rigorous…
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…
We introduce adaptive particle refinement for compressible smoothed particle hydrodynamics (SPH). SPH calculations have the natural advantage that resolution follows mass, but this is not always optimal. Our implementation allows the user…
Using adaptive algorithms, the design of nano-scale dielectric structures for photonic applications is explored. Widths of dielectric layers in a linear array are adjusted to match target responses of optical transmission as a function of…
Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline "interpolation" (on the lines of a grid) as an alternative to polynomial spline interpolation (at…