Related papers: Stable and Accurate Interpolation Operators for Hi…
This paper presents a general framework of high-order finite difference (HFD) schemes for the tempered fractional Laplacian (TFL) based on new generating functions obtained from the discrete symbols. Specifically, for sufficiently smooth…
The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines,…
In this paper, a new class of \emph{Taylor-accelerated neural network interpolation operators} is introduced on quasi-uniform irregular grids. These operators improve existing neural network interpolation operators by incorporating Taylor…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
Inverter-based microgrids are an important technology for sustainable electrical power systems and typically use droop-controlled grid-forming inverters to interface distributed energy resources to the network and control the voltage and…
Only a few numerical methods can treat boundary value problems on polygonal and polyhedral meshes. The BEM-based Finite Element Method is one of the new discretization strategies, which make use of and benefits from the flexibility of these…
Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
It is an established fact that a finite difference operator approximates a derivative with a fixed algebraic rate of convergence. Nevertheless, we exhibit a new finite difference operator and prove it has spectral accuracy. Its rate of…
The construction of conformal blocks for the analysis of multipoint correlation functions with $N > 4$ local field insertions is an important open problem in higher dimensional conformal field theory. This is the first in a series of papers…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
The stability of non-isolated equilibria to quasilinear parabolic problems of the form $u' = A(u)u + f(u)$ is established in interpolation spaces (and thus extending previous results relying on maximal regularity). The approach allows full…
We present a novel approach of discretizing variable coefficient diffusion operators in the context of meshfree generalized finite difference methods. Our ansatz uses properties of derived operators and combines the discrete Laplace…
In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the…
Block encoding lies at the core of many existing quantum algorithms. Meanwhile, efficient and explicit block encodings of dense operators are commonly acknowledged as a challenging problem. This paper presents a comprehensive study of the…
The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…
Gaussian radial basis functions can be an accurate basis for multivariate interpolation. In practise, high accuracies are often achieved in the flat limit where the interpolation matrix becomes increasingly ill-conditioned. Stable…
The paper presents high-order accurate, energy-, and entropy-stable discretizations constructed from summation-by-parts (SBP) operators. Notably, the discretizations assemble global SBP operators and use continuous solutions, unlike…
It is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products. We give a new algorithm by evaluation and interpolation which is faster than…
Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…