Related papers: Spherical Essentially Non-Oscillatory (SENO) Inter…
Hand-drawn 2D animation workflow is typically initiated with the creation of sketch keyframes. Subsequent manual inbetweens are crafted for smoothness, which is a labor-intensive process and the prospect of automatic animation sketch…
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\em in both space and time}.Such PDE…
Properties and applications of a plasmonic cross-shaped nano-antenna is presented and compared to those of array of holes. A simple analytical model based on the superposition of waves are proposed and compared to the numerical results. A…
This work is dedicated to the development and comparison of WENO-type reconstructions for hyperbolic systems of balance laws. We are particularly interested in high order shock capturing non-oscillatory schemes with uniform accuracy within…
We introduce an efficient numerical method for second order linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. In oscillatory regions the solution is generated via a nonoscillatory…
Interpolation for scattered data is a classical problem in numerical analysis, with a long history of theoretical and practical contributions. Recent advances have utilized deep neural networks to construct interpolators, exhibiting…
The Newton-Schulz (NS) iteration has become a key technique for orthogonalization in optimizers such as Muon and for optimization on the Stiefel manifold. Despite its effectiveness, the conventional NS iteration incurs significant…
This paper presents a novel intersection-based remapping method for isoparametric curvilinear meshes within the indirect arbitrary Lagrangian-Eulerian (ALE) framework, addressing the challenges of transferring physical quantities between…
ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth…
Geospatial interpolation is a challenging task due to real world data often being sparse, heterogeneous and inconsistent. For that matter, this work presents SkNNI, a spherical interpolation algorithm capable of working with such…
We develop interpolation error estimates for general order standard and serendipity edge and face virtual elements in two and three dimensions. Contextually, we investigate the stability properties of the associated L2 discrete bilinear…
In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear…
We revisit the problem of solving the one-dimensional wave equation on a domain with moving boundary. In J. Math. Phys. 11, 2679 (1970), Moore introduced an interesting method to do so. As only in rare cases, a closed analytical solution is…
Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al.\ that combines real algebraic geometry and…
A novel method for SPECT angle interpolation based on deep learning methodologies is presented. Projection data from software phantoms were used to train the proposed model. For evaluation of the efficacy of the method, phantoms based on…
The sensitivity of perturbation sensing can be effectively enhanced with higher-order exceptional points due to the nonlinear response to frequency splitting. However, the experimental implementation is challenging since all the parameters…
We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be…
We consider two nonlinear El Nino Southern Oscillation (ENSO) model to obtain approximate solutions with differential transform method for the first time. Efficiency, accuracy and error rates of solutions are compared with analytic…
We present an approach to constructing a practical coarsening algorithm and interpolation operator for the algebraic multigrid (AMG) method, tailored towards systems of partial differential equations (PDEs) with large near-kernels, such as…
In this paper, a new extrapolation economy cascadic multigrid method is proposed to solve the image restoration model. The new method combines the new extrapolation formula and quadratic interpolation to design a nonlinear prolongation…