Block Preconditioning Techniques for Geophysical Electromagnetics

2020 ◽  
Vol 42 (3) ◽  
pp. B696-B721
Author(s):  
H. Bin Zubair Syed ◽  
C. Farquharson ◽  
S. MacLachlan
Keyword(s):  
Preconditioning Techniques ◽  
Block Preconditioning

A Novel Efficient Numerical Solution of Poisson's Equation for Arbitrary Shapes in Two Dimensions

2016 ◽  
Vol 20 (5) ◽  
pp. 1381-1404
Author(s):  
Zu-Hui Ma ◽  
Weng Cho Chew ◽  
Li Jun Jiang
Keyword(s):  
Mixed Boundary ◽  
Neumann Boundary ◽  
Two Dimensions ◽  
Poisson’S Equation ◽  
Helmholtz Decomposition ◽  
Poisson's Equation ◽  
Preconditioning Techniques ◽  
Decomposition Scheme ◽  
Poisson Solver ◽  
Electric Flux

AbstractEven though there are various fast methods and preconditioning techniques available for the simulation of Poisson problems, little work has been done for solving Poisson's equation by using the Helmholtz decomposition scheme. To bridge this issue, we propose a novel efficient algorithm to solve Poisson's equation in irregular two dimensional domains for electrostatics through a quasi-Helmholtz decomposition technique—the loop-tree basis decomposition. It can handle Dirichlet, Neumann or mixed boundary problems in which the filling media can be homogeneous or inhomogeneous. A novel point of this method is to first find the electric flux efficiently by applying the loop-tree basis functions. Subsequently, the potential is obtained by finding the inverse of the gradient operator. Furthermore, treatments for both Dirichlet and Neumann boundary conditions are addressed. Finally, the validation and efficiency are illustrated by several numerical examples. Through these simulations, it is observed that the computational complexity of our proposed method almost scales as , where N is the triangle patch number of meshes. Consequently, this new algorithm is a feasible fast Poisson solver.

Preconditioning Techniques for Nonsymmetric Linear Systems in the Computation of Incompressible Flows

2009 ◽  
Vol 76 (2) ◽  
Author(s):  
Murat Manguoglu ◽  
Ahmed H. Sameh ◽  
Faisal Saied ◽  
Tayfun E. Tezduyar ◽  
Sunil Sathe
Keyword(s):  
Linear Systems ◽  
Krylov Subspace ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Handling Time ◽  
Navier Stokes ◽  
Preconditioning Techniques ◽  
Navier Stokes Equations ◽  
Nonsymmetric Linear Systems ◽  
Steady State Solutions

In this paper we present effective preconditioning techniques for solving the nonsymmetric systems that arise from the discretization of the Navier–Stokes equations. These linear systems are solved using either Krylov subspace methods or the Richardson scheme. We demonstrate the effectiveness of our techniques in handling time-accurate as well as steady-state solutions. We also compare our solvers with those published previously.

scholarly journals A Parallel Adaptive Newton-Krylov-Schwarz Method for 3D Compressible Inviscid Flow Simulations

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Marzio Sala ◽  
Pénélope Leyland ◽  
Angelo Casagrande
Keyword(s):  
Compressible Flows ◽  
Time Derivative ◽  
Inviscid Flow ◽  
Implicit Time ◽  
Residual Distribution ◽  
Preconditioning Techniques ◽  
Flow Simulations ◽  
Efficient Data ◽  
Time Marching ◽  
2D And 3D

A parallel adaptive pseudo transient Newton-Krylov-Schwarz (αΨNKS) method for the solution of compressible flows is presented. Multidimensional upwind residual distribution schemes are used for space discretisation, while an implicit time-marching scheme is employed for the discretisation of the (pseudo)time derivative. The linear system arising from the Newton method applied to the resulting nonlinear system is solved by the means of Krylov iterations with Schwarz-type preconditioners. A scalable and efficient data structure for theαΨNKS procedure is presented. The main computational kernels are considered, and an extensive analysis is reported to compare the Krylov accelerators, the preconditioning techniques. Results, obtained on a distributed memory computer, are presented for 2D and 3D problems of aeronautical interest on unstructured grids.

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