Related papers: Adaptive Partition of Unity Interpolation Method w…
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
Partition of unity methods (PUMs) on graphs represent straightforward and remarkably adaptable auxiliary techniques for graph signal processing. By relying solely on the intrinsic graph structure, we propose the generation of a partition of…
The interpolation on Grassmann manifolds in the framework of parametric evolution partial differential equations is presented. Interpolation points on the Grassmann manifold are the subspaces spanned by the POD bases of the available…
In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that,…
Standard video frame interpolation methods first estimate optical flow between input frames and then synthesize an intermediate frame guided by motion. Recent approaches merge these two steps into a single convolution process by convolving…
We present a new adaptive collocation scheme for solving partial differential equations based on Local Coupled Multiquadrics (LCMQs) within a covers-and-nodes framework. The method, referred to as the Adaptive Ch Method, automatically…
In this paper we present an efficient algorithm for bivariate interpolation, which is based on the use of the partition of unity method for constructing a global interpolant. It is obtained by combining local radial basis function…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
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…
As Deep Neural Networks are becoming more popular, much of the attention is being devoted to Computer Vision problems that used to be solved with more traditional approaches. Video frame interpolation is one of such challenges that has seen…
We present a semi-Lagrangian method for the numerical resolution of Vlasov-type equations on multi-patch meshes. Following N. Crouseilles et al. [A parallel Vlasov solver based on local cubic spline interpolation on patches. Journal of…
In this paper a novel hybrid approach for compensating the distortion of any interpolation has been proposed. In this hybrid method, a modular approach was incorporated in an iterative fashion. By using this approach we can get drastic…
The Closest Point method, initially developed by Ruuth and Merriman, allows for the numerical solution of surface partial differential equations without the need for a parameterization of the surface itself. Surface quantities are embedded…
We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear programming, our method is based on a dynamical formulation…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
Intramolecular symmetry-adapted perturbation theory (ISAPT) is a method to compute and decompose the noncovalent interaction energy between two molecular fragments A and B connected via a linker C. The existing ISAPT algorithm displays…
Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the smaller error of approximation. The question of constructing…
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 present a local interpolation method in four dimensions utilising cubic splines. An extension of the three-dimensional tricubic method, the interpolated function has C$^1$ continuity and its partial derivatives are analytically…