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In this paper, we propose different algorithms for the solution of a tensor linear discrete ill-posed problem arising in the application of the meshless method for solving PDEs in three-dimensional space using multiquadric radial basis…
In the present paper, we study the existence and uniqueness of solutions to some nonlocal singular elliptic problem under Dirichlet boundary condition. Problem is settled in Musielak-Sobolev spaces.
The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…
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…
The dual-primal isogeometric tearing and interconnecting (IETI-DP) method is the adaption of the dual-primal finite element tearing and interconnecting (FETI-DP) method to isogeometric analysis of scalar elliptic boundary value problems…
A challenge in multivariate problems with discrete structures is the inclusion of prior information that may differ in each separate structure. A particular example of this is seismic amplitude versus angle (AVA) inversion to elastic…
Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and computation-intensive numerical simulations…
We consider large linear systems arising from the isogeometric discretization of the Poisson problem on a single-patch domain. The numerical solution of such systems is considered a challenging task, particularly when the degree of the…
This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually…
In an unnormalized Krylov subspace framework for solving symmetric systems of linear equations, the orthogonal vectors that are generated by a Lanczos process are not necessarily on the form of gradients. Associating each orthogonal vector…
The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condition number of the system matrix not only grows with the…
We use the Calogero equation to illustrate the following two aspects of the Painleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the Painleve test for integrability, the singular expansions of its solutions around…
A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and…
Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points. For multidimensional…
A local approach to the time integration of PDEs by exponential methods is proposed, motivated by theoretical estimates by A.Iserles on the decay of off-diagonal terms in the exponentials of sparse matrices. An overlapping domain…
Regularized least-squares approaches have been successfully applied to linear system identification. Recent approaches use quadratic penalty terms on the unknown impulse response defined by stable spline kernels, which control model space…
Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find…
In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based on them. These methods allow to solve the linear system…
Partial differential equations with distributional sources---in particular, involving (derivatives of) delta distributions---have become increasingly ubiquitous in numerous areas of physics and applied mathematics. It is often of…