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Showing 1 to 19 of 19 for “"Schur Complement"”.
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Approximation of Generalized Schur Complements (Ladder Network)
The Schur complement of a linear operator on a finite dimensional Hilbert space is discussed and six generalizations are presented. Conditions are established under which these generalizations are equivalent. The infinite dimensional case is then considered and counterexamples are given to show …
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Hessian Matrix-Free Lagrange-Newton-Krylov-Schur-Schwarz Methods for Elliptic Inverse Problems
… an inner-outer structure, taking the form of a Schur complement (block factorization) at the outer level and Schwarz projections at the inner level. However, building an exact Schur complement is prohibitively expensive. Thus, we use Schur complement approximations, including the identity, …
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Computation of multiscale time-harmonic electromagnetic radiation
… or high-frequency asymptotic methods through a Schur complement analysis of the continuous and discretized equations. The proposed Schur complement EPA-PO hybrid introduces clear physics with applicability to other formulations for the individual domains. The proposed hybrid also maps the PO …
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A Modified Preconditioned Conjugate Gradient Method for Approximating the Scattering Amplitude
… positive spectrum. We investigate the use of Schur Complement preconditioners with block-diagonal factorization to speed up the convergence of our method and compare the results to our NspcG method without preconditioning.</p>
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Trace finite element method for material surface flows
… Eigenvalue bounds for the preconditioned Schur complement are derived. Properties of the proposed method are illustrated with numerical examples which include simulation of Kelvin--Helmholtz instability at different Reynolds numbers on a sphere and torus, as well as tangential flow induced …
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Domain Decomposition Methods for Convection-Diffusion-Reaction Equations with Finite Volume Discretizations
… DD methods, some preconditioners based on the Schur complement with low-rank corrections (SLR) are introduced. A time independent CDR model with the second-order finite volume discretization is studied by applying these non-overlapping DD preconditioners. In both overlapping and non-overlapping …
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An iterative pressure-correction method for the unsteady incompressible Navier-Stokes Equation
… Richardson iterative method for the pressure- Schur complement equation. Typical pressure correction methods perform only one iteration and suffer from a splitting error that results in a spurious numerical boundary layer, and a limited order of convergence in time. We investigate the benefit …
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Local polynomial chaos expansion method for high dimensional stochastic differential equations
… locally. An establishment is made between Schur complement in traditional domain decomposition setting and the local PCE method at the coupling stage. A further branch of discussion on the topic of decoupling strategy is presented at the end to propose some of the intuitive possibilities of …
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Developments in the Extended Finite Element Method and Algebraic Multigrid for Solid Mechanics Problems Involving Discontinuities
… are presented. In the first approach, the Schur complement of the linear system arising from XFEM is used to develop a Hybrid-AMG method such that crack-conforming aggregates are formed. Another alternative approach involves transforming the original linear system into a modified system …
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Geometric Computing beyond the Laplacian
… operator, the Dirichlet-to-Neumann operator—the Schur complement of a higher dimensional Laplacian with the interior marginalized out. In addition, we develop discrete models of inverse elliptic problems, resembling core properties of the continuous counterparts. With extensive experimental …
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Scaling finite difference methods in large eddy simulation of jet engine noise to the petascale: numerical methods and their efficient and automated implementation
… (LES) is a robust and accurate tool that complements the existing theoretical and experimental approaches. In order to satisfy the stringent requirements of CAA on numerical accuracy, finite difference methods in LES-based jet engine noise prediction rely on the implicitly formulated …
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Dynamic Modeling and Real-time Simulation of Power Electronics-dominated Power Grids Using Hybrid DDM and EDDM Techniques
… with separate computations performed using the Schur-complement technique. Simulations on test systems with up to 25,000 buses, 8,000 synchronous generators, and 256 PV farms demonstrate a notable 7.8x acceleration in speed when executed on an NVIDIA GeForce RTX 2070 SUPER GPU, thanks to a …
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Modeling and control of cadmium zinc telluride grown via an electro-dynamic gradient freeze furnace.
… models as if they were one monolithic model. A Schur complement formulation is employed to solve the free-boundary problem associated with melt crystal growth systems. With this form, the difficult interface location part of the problem is mapped away from the equations governing transport. We …
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Multilevel-in-Time Methods for Optimal Control of PDEs and Training of Recurrent Neural Networks
… resulting two-grid iteration is interpreted as a Schur complement iteration. This allows its extension to a multigrid iteration and it also reveals how to derive a preconditioner for use in a Krylov subspace methods. The performance of the multigrid iterations as well as of flexible GMRES with the …
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A high-order hybrid flow solver for the simulation of nonlinear internal waves in long complex domains
… pressure Poisson equation (PPE). The resulting Schur complement system of equations of the PPE is iteratively solved using a deflated block-Jacobi preconditioned conjugate gradient solver which ensures a fast convergence rate independent of the domain's aspect-ratio, the number of elements in …
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Level set methods for higher order evolution laws
… second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the …
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Domain Decomposition Preconditioners for Hermite Collocation Problems
Accelerating the convergence rate of Krylov subspace methods with parallelizable preconditioners is essential for obtaining effective iterative solvers for very large linear systems of equations. Substructuring provides a framework for constructing robust and parallel preconditioners for linear …
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ON THE LYAPUNOV-TYPE DIAGONAL STABILITY
… enhanced statement of this result based on the Schur complement formulation is presented here along with a shorter and purely matrix-theoretic proof. We develop a number of extensions to this result, and formulate the range of feasible common diagonal Lyapunov solutions. In particular, we derive …
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The solution of large viscoelastic flow problems using parallel iterative techniques
… The parallel preconditioner, called the Block Complement and Additive Levels Method (BCALM) preconditioner, is based on treating pressure unknowns separately from the variables velocities and gradients. A pressure preconditioner is constructed from a factor of the Schur complement of the …