Related papers: On False Accuracy Verification of UMUSCL Scheme
Concurrent multiscale methods play an important role in modeling and simulating materials with defects, aiming to achieve the balance between accuracy and efficiency. Atomistic-to-continuum (a/c) coupling methods, a typical class of…
We identify a property of renormalizable SU(N)/U(1) gauge theories, the intrinsic Conformality ($iCF$), which underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional…
In this paper, a centred universal high-order finite volume method for solving hyperbolic balance laws is presented. The scheme belongs to the family of ADER methods where the Generalized Riemann Problems (GRP) is a building block. The…
The use of the dimensional regularization in the on-mass-shell renormalization scheme sometimes fails to locally cancel the ultraviolet divergence for a class of diagrams in the two-loop order. The mechanism is discussed based on an example…
We analyze the behavior of the Euler method for delay differential equations under nonstandard assumptions on the right-hand-side function f, when evaluations of f are corrupted by informational noise. We provide theoretical upper bounds on…
The transition between the two phases of 4D Euclidean Dynamical Triangulation [1] was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems [3,4]. However, one may wonder if this…
Testing the order of accuracy of (very) high order methods for shallow water (and Euler) equations is a delicate operation and the test cases are the crucial starting point of this operation. We provide a short derivation of vortex-like…
Three non-equilibrium photoionisation algorithms for hydrodynamical grid-based simulation codes are compared in terms of accuracy, timestepping criteria, and parallel scaling. Explicit methods with first-order time accuracy for photon…
As we found previously, when critical points occur within grid intervals, the accuracy relations of smoothness indicators of WENO-JS would differ from that assuming critical points occurring on grid nodes, and accordingly the global…
Deep learning classification models for medical image analysis often perform well on data from scanners that were used during training. However, when these models are applied to data from different vendors, their performance tends to drop…
In this paper, we consider finite difference approximations of the second order wave equation. We use finite difference operators satisfying the summation-by-parts property to discretize the equation in space. Boundary conditions and grid…
Graph-structured datasets often suffer from class imbalance, which complicates node classification tasks. In this work, we address this issue by first providing an upper bound on population risk for imbalanced transductive node…
In this article, we propose a MUSCL-Hancock-type second-order scheme for the discretization of a general class of non-local conservation laws and present its convergence analysis. The main difficulty in designing a MUSCL-Hancock-type scheme…
With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…
The spurious states found in numerical implementations of envelope function models for semiconductor heterostructures and nanostructures are artifacts of the use of the centered-difference formula. They are readily removed by employing a…
We elucidate the origin of large differences (two-fold or more) in the fixed-node errors between the first- vs second-row systems for single-configuration trial wave functions in quantum Monte Carlo calculations. This significant difference…
Micromagnetics depends on high-fidelity numerical methods for magnetization dynamics. This work proposes a third-order temporal accuracy scheme for the Landau-Lifshitz-Gilbert equation, addressing accuracy-efficiency trade-offs in existing…
Using techniques from harmonic analysis, we derive several sharp stability estimates for the second order Heisenberg Uncertainty Principle. We also present the explicit lower and upper bounds for the sharp stability constants and compute…
This work investigates the accuracy and numerical stability of CUR decompositions with oversampling. The CUR decomposition approximates a matrix using a subset of columns and rows of the matrix. When the number of columns and the rows are…
The electroweak diboson production cross-sections are known to receive large radiative corrections beyond leading-order (LO), approaching up to 60% at next-to-leading order (NLO), compared to the scale uncertainties which are in the range…