Marcos A. D. Martins

Simple zero thickness kinematically consistent interface elements

Abstract Interface finite elements have been used in many geotechnical and engineering applications. Essentially, these elements must allow relative displacements between two bodies in contact, or separated by a thin material layer. Frequently, interface elements behave as linear elastic bodies up to a limiting stress state. This linear behavior of interfaces is very important, because it will establish when the slip and/or separation occurs, causing stress redistribution over the mesh. In this paper, the mechanical behavior of interface elements is discussed. It is shown that the kinematic inconsistency pointed by Kaliakin and Li [Comp. Geotech. 17 (1995) 225] for the element proposed by Goodman et al. [ASCE J. Soil Mech. Fdns. Div. 99 (1968) 637] also occurs for other interface models, and new interface elements for 2D and 3D analyses without kinematic inconsistencies are proposed.

Parallel edge-based inexact newton solution of steady incompressible 3D navier-stokes equations

The parallel edge-based solution of 3D incompressible Navier-Stokes equations is presented. The governing partial differential equations are discretized using the SUPG/PSPG stabilized finite element method [5] on unstructured grids. The resulting fully coupled nonlinear system of equations is solved by the inexact Newton-Krylov method [1]. Matrix-vector products within GMRES are computed edge-by-edge, diminishing flop counts and memory requirements. The non-linear solver parallel implementation is based in message passing interface (MPI). Performance tests on several computers, such as the SGI Altix, the Cray XD1 and a mini-wireless cluster were carried out in representative problems and results have shown that edge-based schemes require less CPU time and memory than element-based solutions.

Computational Techniques for Stabilized Edge-Based Finite Element Simulation of Nonlinear Free-Surface Flows

Free-surface flows occur in several problems in hydrodynamics, such as fuel or water sloshing in tanks, waves breaking in ships, offshore platforms, harbors, and coastal areas. The computation of such highly nonlinear flows is challenging, since free-surfaces commonly present merging, fragmentation, and breaking parts, leading to the use of interface-capturing Eulerian approaches. In such methods the surface between two fluids is captured by the use of a marking function, which is transported in a flow field. In this work we discuss computational techniques for efficient implementation of 3D incompressible streamline-upwind/Petrov–Galerkin (SUPG)/pressure-stabilizing/Petrov–Galerkin finite element methods to cope with free-surface problems with the volume-of-fluid method (Elias, and Coutinho, 2007, “Stabilized Edge-Based Finite Element Simulation of Free-Surface Flows,” Int. J. Numer. Methods Fluids, 54, pp. 965–993). The pure advection equation for the scalar marking function was solved by a fully implicit parallel edge-based SUPG finite element formulation. Global mass conservation is enforced, adding or removing mass proportionally to the absolute value of the normal velocity of the interface. We introduce parallel edge-based data structures, a parallel dynamic deactivation algorithm to solve the marking function equation only in a small region around the interface. The implementation is targeted to distributed memory systems with cache-based processors. The performance and accuracy of the proposed solution method is tested in the simulation of the water impact on a square cylinder and in the propagation of a solitary wave.

Edge-based interface elements for solution of three-dimensional geomechanical problems

An edge-based three-dimensional interface element for simulation of joints, faults and other discontinuities present in several geomechanical applications is proposed. Edge-based data structures are used to improve computational efficiency of Inexact Newton methods for solving finite element nonlinear problems on unstructured meshes. Numerical experiments in the solution of three-dimensional problems in cache based and vector processors have shown that memory and computer time are reduced.

Inexact Newton-type methods for non-linear problems arising from the SUPG/PSPG solution of steady incompressible navier-stokes equations

Equations finite element discretization of the incompress ible steady-state Navier-Stokes equations yields a non-linear problem, due to the c onvective terms in the momentum equations. Several methods may be used to solve thi s non-linear problem. In this work we study Inexact Newton-type methods, associated with the SUPG/PSPG stabilized finite element formulation. The resulting systems of equat ions are solved iteratively by a preconditioned Krylov-space method such as GMRES. N umerical experiments are shown to validate our approach. Performance of the nonlin ear strategies is accessed by numerical tests. We concluded that Inexact Newton-t ype methods are more efficient than conventional Newton-type methods.

Parallel Edge-Based Finite Element Techniques for Nonlinear Solid Mechanics

Parallel edge-based data structures are used to improve computational efficiency of Inexact Newton methods for solving finite element nonlinear solid mechanics problems on unstructured meshes composed by tetrahedra or hexaedra. We found that for tetrahedral meshes, the use of edge-based data structures reduce memory requirements to hold the stiffness matrix by a factor of 7, and the number of floating point operations to compute the matrix-vector product needed in the iterative driver of the Inexact Newton method by a factor of 5. For hexahedral meshes the reduction factors are respectively 2 and 3.

Edgepack: a parallel vertex and node reordering package for optimizing edge-based computations in unstructured grids

A new and simple method is proposed to choose the best data configuration in terms of processing phase time according to previous probing of edge-based matrix-vector products for codes using iterative solvers in unstructured grid problems. This method is realized as a suite of routines named EdgePack, acting during both pre-solution and solution phase, based on data locality optimization techniques and variations of matrix-vector product algorithm. Results have been demonstrating the great flexibility and simplicity of this method, which is suitable for distributed memory platforms in which different data configurations can coexist.