Scalable Parallel Newton-Krylov Solvers for Discontinuous Galerkin Discretizations

Persson, Per‐Olof

doi:10.2514/6.2009-606

Cited by 23 publications

(23 citation statements)

References 19 publications

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“…Note, the iteration count is largely independent of the size of the subdomain, the interpolation order, and the choice of constraints. Thus, in the advection limit, a partitioning strategy based on capturing the strong characteristics, such as those used in [39,40], is expected to improve the performance of the preconditioner. However, these strategies are sequential in nature and tend to increase the communication volume, especially in three dimensions.…”

Section: Advection-diffusion Equation: Isotropic Meshmentioning

confidence: 99%

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BDDC preconditioning for high-order Galerkin Least-Squares methods using inexact solvers

Yano

Darmofal

2010

Computer Methods in Applied Mechanics and Engineering

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a b s t r a c tA high-order Galerkin Least-Squares (GLS) finite element discretization is combined with a Balancing Domain Decomposition by Constraints (BDDC) preconditioner and inexact local solvers to provide an efficient solution technique for large-scale, convection-dominated problems. The algorithm is applied to the linear system arising from the discretization of the two-dimensional advection-diffusion equation and Euler equations for compressible, inviscid flow. A Robin-Robin interface condition is extended to the Euler equations using entropy-symmetrized variables. The BDDC method maintains scalability for the high-order discretization of the diffusion-dominated flows, and achieves low iteration count in the advection-dominated regime. The BDDC method based on inexact local solvers with incomplete factorization and p = 1 coarse correction maintains the performance of the exact counterpart for the wide range of the Peclet numbers considered while at significantly reduced memory and computational costs.

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Section: Advection-diffusion Equation: Isotropic Meshmentioning

confidence: 99%

“…The degradation in the preconditioner performance suggests the partitioning strategy that considers the direction of characteristics and minimizes the number of times a characteristic enters different subdomains, e.g. strategies considered in [39,40], may be more important for unstructured meshes.…”

Section: Advection-diffusion Equation: Unstructured Meshesmentioning

confidence: 99%

BDDC preconditioning for high-order Galerkin Least-Squares methods using inexact solvers

Yano

Darmofal

2010

Computer Methods in Applied Mechanics and Engineering

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“…For the high-fidelity simulations, we use the 3DG code [37,38,39,40,41,42], which implements a high-order accurate discontinuous Galerkin method to solve the compressible Navier-Stokes equations on unstructured meshes of tetrahedra. Although the flow is nearly incompressible, the use of a compressible flow formulation has the advantage of providing high-order accuracy in time with regular ODE time integrators.…”

Section: Discontinuous Galerkin Arbitrary Lagrangian-eulerian (Ale) Nmentioning

confidence: 99%

“…It is clear that parallel computers are needed, both for storing these matrices and to perform the computations. The parallel 3DG code [40] is based on the MPI interface, and runs on parallel computer clusters. The domain is decomposed using the METIS software [51] and the discretization and matrix assembly is done in parallel.…”

Section: Parallel Newton-krylov Solversmentioning

confidence: 99%

Numerical simulation of flapping wings using a panel method and a high‐order Navier–Stokes solver

Persson

Willis

Peraire

2012

Numerical Meth Engineering

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SUMMARYThe design of efficient flapping wings for human engineered micro aerial vehicles (MAVs) has long been an elusive goal, in part due to the large size of the design space. One strategy for overcoming this difficulty is to use a multi-fidelity simulation strategy appropriately balances computation time and accuracy. We compare two models with different geometric and physical fidelity. The low-fidelity model is an inviscid doublet lattice method with infinitely thin lifting surfaces. The high-fidelity model is a high-order accurate discontinuous Galerkin Navier-Stokes solver which uses an accurate representation of the flapping wing geometry. To compare the performance of the two methods, we consider a model flapping wing with an elliptical planform and an analytically prescribed spanwise wing twist, at size scales relevant to MAVs. Our results show that in many cases, including those with mild separation, low fidelity simulations can accurately predict integrated forces, provide insight into the flow structure, indicate regions of likely separation and shed light on design relevant quantities. But for problems with significant levels of separation, higher fidelity methods are required to capture the details of the flow-field. Inevitably high-fidelity simulations are needed to establish the limits of validity of the lower fidelity simulations.

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“…The resulting discretizations from the space-time DG method are higher-dimensional and fully implicit, and we solve the resulting nonlinear systems of equations using efficient parallel NewtonKrylov solvers [45,46]. We generate high-quality moving meshes using the DistMesh algorithm [47], and construct the space-time elements for each layer of timesteps using a local construction.…”

Section: Introductionmentioning

confidence: 99%

A high-order discontinuous Galerkin method with unstructured space–time meshes for two-dimensional compressible flows on domains with large deformations

Wang

Persson

2015

Computers & Fluids

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a b s t r a c tWe present a high-order accurate space-time discontinuous Galerkin method for solving twodimensional compressible flow problems on fully unstructured space-time meshes. The discretization is based on a nodal formulation, with appropriate numerical fluxes for the first and the second-order terms, respectively. The scheme is implicit, and we solve the resulting non-linear systems using a parallel Newton-Krylov solver. The meshes are produced by a mesh moving technique with element connectivity updates, and the corresponding space-time elements are produced directly based on these local operations. To obtain globally conforming tetrahedral meshes, we first derive the required conditions on a prism boundary mesh to allow for a valid local triangulation. Next, we present an efficient algorithm for finding a global mesh that satisfies these conditions. We also show how to add and remove mesh nodes, again using local constructs for the space-time mesh. Our method is demonstrated on a number of test problems, showing the high-order accuracy for model problems, and the ability to solve flow problems on domains with complex large deformations.

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Scalable Parallel Newton-Krylov Solvers for Discontinuous Galerkin Discretizations

Cited by 23 publications

References 19 publications

BDDC preconditioning for high-order Galerkin Least-Squares methods using inexact solvers

BDDC preconditioning for high-order Galerkin Least-Squares methods using inexact solvers

Numerical simulation of flapping wings using a panel method and a high‐order Navier–Stokes solver

A high-order discontinuous Galerkin method with unstructured space–time meshes for two-dimensional compressible flows on domains with large deformations

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