Related papers: A Partition of Unity Method for Divergence-free or…
In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as a special case, which enables us to effectively find the optimal value of the RBF shape parameter. In…
This work uses vector field inequalities (VFI) to prevent robot self-collisions and collisions with the workspace. Differently from previous approaches, the method is suitable for both velocity and torque-actuated robots. We propose a new…
Recent progress in large-scale scene rendering has yielded Neural Radiance Fields (NeRF)-based models with an impressive ability to synthesize scenes across small objects and indoor scenes. Nevertheless, extending this idea to large-scale…
This paper deals with a numerical analysis of plastic deformation under various conditions, utilizing Radial Basis Function (RBF) approximation. The focus is on the elasto-plastic von Mises problem under plane-strain assumption. Elastic…
Runge--Kutta (RK) methods are widely used techniques for solving a class of initial value problems. In this article, we introduce an adaptive multiquadratic (MQ) radial basis function (RBF)-based method to develop enhanced explicit RK…
Kernel-based classification methods, particularly the support vector machine (SVM), are among the most common algorithms for hyperspectral data classification. The Radial Basis function (RBF) kernel has earned great popularity in…
The design of RFIC often involves exploring a large number of design variations in an invariant background composed of the processing stack and unchanged circuit blocks. Conventional electromagnetic solvers require a full-domain simulation…
This work develops optimal preconditioners for the discrete H(curl) and H(div) problems on two-dimensional surfaces by nodal auxiliary space preconditioning [R. Hiptmair, J. Xu: SIAM J. Numer. Anal. \textbf{45}, 2483-2509 (2007)]. In…
In electromagnetic simulations of magnets and machines one is often interested in a highly accurate and local evaluation of the magnetic field uniformity. Based on local post-processing of the solution, a defect correction scheme is…
Partition of unity methods (PUMs) on graphs are simple and highly adaptive auxiliary tools for graph signal processing. Based on a greedy-type metric clustering and augmentation scheme, we show how a partition of unity can be generated in…
In this paper, we propose a method to segment and recover a static, clean background and multiple 360$^\circ$ objects from observations of scenes at different timestamps. Recent works have used neural radiance fields to model 3D scenes and…
Very few studies involve how to construct the efficient RBFs by means of problem features. Recently the present author presented general solution RBF (GS-RBF) methodology to create operator-dependent RBFs successfully [1]. On the other…
The random Fourier features (RFFs) method is a powerful and popular technique in kernel approximation for scalability of kernel methods. The theoretical foundation of RFFs is based on the Bochner theorem that relates symmetric, positive…
Strong-form meshless methods received much attention in recent years and are being extensively researched and applied to a wide range of problems in science and engineering. However, the solution of elasto-plastic problems has proven to be…
Neural Radiance Fields (NeRF) has emerged as a compelling framework for scene representation and 3D recovery. To improve its performance on real-world data, depth regularizations have proven to be the most effective ones. However, depth…
Polynomial reproduction plays a relevant role in deriving error estimates for various approximation schemes. Local reproduction in a quasi-uniform setting is a significant factor in the estimation of error and the assessment of stability…
In modern computer vision, the optimal representation of 3D shape continues to be task-dependent. One fundamental operation applied to such representations is differentiable rendering, as it enables inverse graphics approaches in learning…
This paper focuses on RBF-based meshless methods for approximating differential operators, one of the most popular being RBF-FD. Recently, a hybrid approach was introduced that combines RBF interpolation and traditional finite difference…
The Lane-Emden type equations are employed in the modelling of several phenomena in the areas of mathematical physics and astrophysics . In this paper a new numerical method is applied to investigate some well-known classes of Lane-Emden…
Neural radiance fields (NeRF) rely on volume rendering to synthesize novel views. Volume rendering requires evaluating an integral along each ray, which is numerically approximated with a finite sum that corresponds to the exact integral…