Related papers: QTT-isogeometric solver in two dimensions
In this article we present a novel and general methodology for building second order finite volume implicit-explicit (IMEX) numerical schemes for solving two dimensional financial parabolic PDEs with mixed derivatives. In particular,…
We propose a fast fourth-order cut cell method for solving constant-coefficient elliptic equations in two-dimensional irregular domains. In our methodology, the key to dealing with irregular domains is the poised lattice generation (PLG)…
The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…
We design and analyze an iterative two-grid algorithm for the finite element discretizations of strongly nonlinear elliptic boundary value problems in this paper. We propose an iterative two-grid algorithm, in which a nonlinear problem is…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…
Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information…
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…
In this article, a fast algorithm based on time two-mesh (TT-M) finite element (FE) scheme, which aims at solving nonlinear problems quickly, is considered to numerically solve the nonlinear space fractional Allen-Cahn equations with smooth…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
We present a new direct logarithmically optimal in theory and fast in practice algorithm to implement the high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. The key points…
This article proposes a new numerical algorithm for second order elliptic equations in non-divergence form. The new method is based on a discrete weak Hessian operator locally constructed by following the weak Galerkin strategy. The…
Computing the stiffness matrix for the finite element discretization of the nonlocal Laplacian on unstructured meshes is difficult, because the operator is nonlocal and can even be singular. In this paper, we focus on the $C^0$-piecewise…
We present multigrid methods for solving elliptic partial differential equations on arbitrary domains using the nodal ghost finite element method, an unfitted boundary approach where the domain is implicitly defined by a level-set function.…
There has been growing interest in high-order tensor methods for nonconvex optimization, with adaptive regularization, as they possess better/optimal worst-case evaluation complexity globally and faster convergence asymptotically. These…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
Isogeometric Analysis (IgA) is a versatile method for the discretization of partial differential equations on complex domains, which arise in various applications of science and engineering. Some complex geometries can be better described…
For smooth finite fields $F_q$ (i.e., when $q-1$ factors into small primes) the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division,…