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In this paper, we propose an augmented subspace based adaptive proper orthogonal decomposition (POD) method for solving the time dependent partial differential equations. By augmenting the POD subspace with some auxiliary modes, we obtain…
We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…
An improved numerical solver for the unified solution of compressible and incompressible fluids involving interfaces is proposed. The present method is based on the CIP-CUP (Cubic Interpolated Propagation / Combined, Unified Procedure)…
For continuous boundary data, including data of polynomial growth, modified Poisson integrals are used to write solutions to the half space Dirichlet and Neumann problems in $\mathbb{R}^{n}$. Pointwise growth estimates for these integrals…
Approximate solutions of linear and nonlinear integral equations using methods related to an interpolatory projection involve many integrals which need to be evaluated using a numerical quadrature formula. In this paper, we consider…
The question of adaptive mesh generation for approximation by splines has been studied for a number of years by various authors. The results have numerous applications in computational and discrete geometry, computer aided geometric design,…
Grids are a general representation for capturing regularly-spaced information, but since they are uniform in space, they cannot dynamically allocate resolution to regions with varying levels of detail. There has been some exploration of…
The problems of computational data processing involving regression, interpolation, reconstruction and imputation for multidimensional big datasets are becoming more important these days, because of the availability of data and their widely…
Adaptive meshes have the potential to improve the accuracy and efficiency of atmospheric modelling by increasing resolution where it is most needed. Mesh re-distribution, or r-adaptivity, adapts by moving the mesh without changing the…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
We present a method to solve two-stage stochastic problems with fixed recourse when the uncertainty space can have either discrete or continuous distributions. Given a partition of the uncertainty space, the method is addressed to solve a…
Video frame interpolation, the synthesis of novel views in time, is an increasingly popular research direction with many new papers further advancing the state of the art. But as each new method comes with a host of variables that affect…
In order to solve Prandtl-type equations we propose a collocation-quadrature method based on VP filtered interpolation at Chebyshev nodes. Uniform convergence and stability are proved in a couple of Holder - Zygmund spaces of locally…
A key scalability challenge in neural solvers for industrial-scale physics simulations is efficiently capturing both fine-grained local interactions and long-range global dependencies across millions of spatial elements. We introduce the…
Adaptive lattice Boltzmann methods (LBMs) are based on velocity discretizations that self-adjust to local macroscopic conditions such as velocity and temperature. While this feature improves the accuracy and the stability of LBMs for large…
We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of…
Slice interpolation is a fast growing field in medical image processing. Intensity-based interpolation and object-based interpolation are two major groups of methods in the literature. In this paper, we describe an object-oriented,…
The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order…
Existing variational mesh functionals often suffer from strong nonlinearity or dependence on empirical parameters.We propose a new variational functional for adaptive moving mesh generation that enforces equidistribution and alignment…
Manifold models consider natural-image patches to be on a low-dimensional manifold embedded in a high dimensional state space and each patch and its similar patches to approximately lie on a linear affine subspace. Manifold models are…