Related papers: An Efficient Algorithm for the Piecewise-Smooth Mo…
A piecewise Pad\'e-Chebyshev type (PiPCT) approximation method is proposed to minimize the Gibbs phenomenon in approximating piecewise smooth functions. A theorem on $L^1$-error estimate is proved for sufficiently smooth functions using a…
Image segmentation algorithms often depend on appearance models that characterize the distribution of pixel values in different image regions. We describe a new approach for estimating appearance models directly from an image, without…
Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a…
Partial differential equations (PDEs) with multiple scales or those defined over sufficiently large domains arise in various areas of science and engineering and often present problems when approximating the solutions numerically. Machine…
In this paper, we consider the problem of piecewise affine abstraction of nonlinear systems, i.e., the overapproximation of its nonlinear dynamics by a pair of piecewise affine functions that "includes" the dynamical characteristics of the…
This work proposes an evolutionary computing-based image segmentation approach for analyzing soundness in Additive Friction Stir Deposition (AFSD) processes. Particle Swarm Optimization (PSO) was employed to determine optimal segmentation…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
When numerically solving partial differential equations (PDEs), the first step is often to discretize the geometry using a mesh and to solve a corresponding discretization of the PDE. Standard finite and spectral element methods require…
Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth. In this paper, we introduce a general class of approximate proximal splitting (APS) methods for solving such minimization…
Partitioning a polygonal mesh into meaningful parts can be challenging. Many applications require decomposing such structures for further processing in computer graphics. In the last decade, several methods were proposed to tackle this…
With the ultimate goal of iteratively solving piecewise smooth (PS) systems, we consider the solution of piecewise linear (PL) equations. PL models can be derived in the fashion of automatic or algorithmic differentiation as local…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
Accurate image segmentation is essential for modern computer vision applications such as image editing, autonomous driving, and medical image analysis. In recent years, Dichotomous Image Segmentation (DIS) has become a standard task for…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
In this paper, we want to clarify the Gibbs phenomenon when continuous and discontinuous finite elements are used to approximate discontinuous or nearly discontinuous PDE solutions from the approximation point of view. For a simple step…
A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in…
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…
Recent advances in deep learning makes solving parabolic partial differential equations (PDEs) in high dimensional spaces possible via forward-backward stochastic differential equation (FBSDE) formulations. The implementation of most…
An extension of the algebraic-geometric method for nonlinear integrable PDE's is shown to lead to new piecewise smooth weak solutions of a class of $N$-component systems of nonlinear evolution equations. This class includes, among others,…
This paper provides a comprehensive study of the nonmonotone forward-backward splitting (FBS) method for solving a class of nonsmooth composite problems in Hilbert spaces. The objective function is the sum of a Fr\'echet differentiable (not…