Related papers: A Full Multigrid Method for Nonlinear Eigenvalue P…
A high precision, and space time fully decoupled, wavelet formulation numerical method is developed for a class of nonlinear initial boundary value problems. This method is established based on a proposed Coiflet based approximation scheme…
Boundary value problems based on the convection-diffusion equation arise naturally in models of fluid flow across a variety of engineering applications and design feasibility studies. Naturally, their efficient numerical solution has…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
In this work, we consider the Dirichlet boundary value problem for nonlinear triharmonic equation. Due to the reduction of the nonlinear boundary value problem to operator equation for the nonlinear term and the unknown second normal…
In this paper we outline a general method for finding well-posed boundary value problems for linear equations of mixed elliptic and hyperbolic type, which extends previous techniques of Berezanskii, Didenko, and Friedrichs. This method is…
The performance of finite element solvers on modern computer architectures is typically memory bound for sufficiently large problems. The main cause for this is that loading matrix elements from RAM into CPU cache is significantly slower…
A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our…
A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the…
In this paper, we consider a boundary value problem (BVP) for a fourth order nonlinear functional integro-differential equation. We establish the existence and uniqueness of solution and construct a numerical method for solving it. We prove…
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for…
A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
This work presents a generalized boundary integral method for elliptic equations on surfaces, encompassing both boundary value and interface problems. The method is kernel-free, implying that the explicit analytical expression of the kernel…
The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…