Related papers: Preconditioned normal equations for solving discre…
This work develops optimal preconditioners for the discrete H(curl) and H(div) problems on two-dimensional surfaces by nodal auxiliary space preconditioning [R. Hiptmair, J. Xu: SIAM J. Numer. Anal. \textbf{45}, 2483-2509 (2007)]. In…
A discussion is presented, within a simple unifying scheme, about different types of symmetry of PDE's, with the introduction and a precise characterization of the notions of "standard" and "weak" conditional symmetries, together with their…
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
The method, proposed in the given work, allows the application of well developed standard methods used in quantum mechanics for approximate solution of the systems of ordinary linear differential equations with periodical coefficients.
We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…
We apply preconditioning, which is widely used in classical solvers for linear systems $A\textbf{x}=\textbf{b}$, to the variational quantum linear solver. By utilizing incomplete LU factorization as a preconditioner for linear equations…
We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove that the solutions can be characterized by well-posed…
In this paper, the generalized shift-splitting preconditioner is implemented for saddle point problems with symmetric positive definite (1,1)-block and symmetric positive semidefinite (2,2)-block. The proposed preconditioner is extracted…
Gr\"obner Bases and Cylindrical Algebraic Decomposition are generally thought of as two, rather different, methods of looking at systems of equations and, in the case of Cylindrical Algebraic Decomposition, inequalities. However, even for a…
Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice and plays an important role in the generalization of modern machine learning. However, prior research has revealed instances where the…
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…
Optimization problems with constraints in the form of a partial differential equation arise frequently in the process of engineering design. The discretization of PDE-constrained optimization problems results in large-scale linear systems…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
This work presents a geometrical formulation of the Clairin theory of conditional symmetries for higher-order systems of partial differential equations (PDEs). We devise methods for obtaining Lie algebras of conditional symmetries from…
Efficient and stable solution of partial differential equations (PDEs) is central to scientific and engineering applications, yet existing numerical solvers rely heavily on matrix based discretizations, while learning based methods require…
The main subject of this paper is the study of analytic second order linear partial differential equations. We aim to solve the classical equations and some more, in the real or complex analytical case. This is done by introducing methods…
This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…
The efficient solution of moderately large-scale linear systems arising from the KKT conditions in optimal control problems (OCPs) is a critical challenge in robotics. With the stagnation of Moore's law, there is growing interest in…
We present a scalable approach to solve a class of elliptic partial differential equation (PDE)-constrained optimization problems with bound constraints. This approach utilizes a robust full-space interior-point (IP)-Gauss-Newton…
The preconditioned iterative solution of large-scale saddle-point systems is of great importance in numerous application areas, many of them involving partial differential equations. Robustness with respect to certain problem parameters is…