Related papers: A Radial Basis Function (RBF)-Finite Difference (F…
Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid makes this approach not feasible for high-dimensional problems…
A computational method for numeric resolution of a PDEs system, based on a Finite Differences schema integrated by interpolations of partial results, and an estimate of the error of its solution respect to the normal FD solution.
A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for…
Parabolic partial differential equations (PDEs) are in ubiquitous, very effective use to model diffusion processes. However, there are many applications (e.g., such as in hydrology, animal foraging, biology, and light diffusion just do name…
We propose an approach to solving partial differential equations (PDEs) using a set of neural networks which we call Neural Basis Functions (NBF). This NBF framework is a novel variation of the POD DeepONet operator learning approach where…
This paper presents a comprehensive experimental validation of a recently developed Ray Deflection Function (RDF) approach, which offers a new framework for modeling surface roughness effects in optical systems. Through detailed geometrical…
Surface reconstruction from a set of scattered points, or a point cloud, has many applications ranging from computer graphics to remote sensing. We present a new method for this task that produces an implicit surface (zero-level set)…
The growing availability of computational resources has significantly increased the interest of the scientific community in performing complex multi-physics and multi-domain simulations. However, the generation of appropriate computational…
Based on the radial basis function (RBF), non-singular general solution and dual reciprocity method (DRM), this paper presents an inherently meshless, integration-free, boundary-only RBF collocation techniques for numerical solution of…
This paper aims to establish a first general error estimate for numerical approximations of the system of reaction-diffusion equations (SRDEs), using reasonable regularity assumptions on the exact solutions. We employ the gradient…
Given only a collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to solve elliptic partial differential equations (PDEs) supplemented with boundary conditions. Notice…
We consider boundary value problems with Riemann-Liouville fractional derivatives of order $s\in (1, 2)$ with non-constant diffusion and reaction coefficients. A variational formulation is derived and analyzed leading to the well-posedness…
Radial basis functions are typically used when discretization sche-mes require inhomogeneous node distributions. While spawning from a desire to interpolate functions on a random set of nodes, they have found successful applications in…
Multiphysics simulations frequently require transferring solution fields between subproblems with non-matching spatial discretizations, typically using interpolation techniques. Standard methods are usually based on measuring the closeness…
Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…
We design and analyze an approximation method for advection-diffusion-reaction equations where the (generalized) degrees of freedom are polynomials of order $k\ge0$ at mesh faces. The method hinges on local discrete reconstruction operators…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
Existing image SR and generic diffusion models transfer poorly to fluid SR: they are sampling-intensive, ignore physical constraints, and often yield spectral mismatch and spurious divergence. We address fluid super-resolution (SR) with…
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack…
We extend Regularised Diffusion-Shock (RDS) filtering from Euclidean space $\mathbb{R}_2$ [1] to position-orientation space $\mathbb{M}_2 \cong \mathbb{R}^2 \times S^1$. This has numerous advantages, e.g. making it possible to enhance and…