FSAI-based parallel Mixed Constraint Preconditioners for saddle point problems arising in geomechanics

In this paper we propose and describe a parallel implementation of a block preconditioner for the solution of saddle point linear systems arising from Finite Element (FE) discretization of 3D coupled consolidation problems. The Mixed Constraint Preconditioner developed in [L. Bergamaschi, M. Ferronato, G. Gambolati, Mixed constraint preconditioners for the solution to FE coupled consolidation equations, J. Comput. Phys., 227(23) (2008), 9885–9897] is combined with the parallel FSAI preconditioner which is used here to approximate the inverses of both the structural (1, 1) block and an appropriate Schur complement matrix. The resulting preconditioner proves effective in the acceleration of the BiCGSTAB iterative solver. Numerical results on a number of test cases of size up to 2×10⁶ unknowns and 1.2×10⁸ nonzeros show the perfect scalability of the overall code up to 256 processors.     

FSAI-based parallel Mixed Constraint Preconditioners for saddle point problems arising in geomechanics

In this paper we propose and describe a parallel implementation of a block preconditioner for the solution of saddle point linear systems arising from Finite Element (FE) discretization of 3D coupled consolidation problems. The Mixed Constraint Preconditioner developed in [L. Bergamaschi, M. Ferronato, G. Gambolati, Mixed constraint preconditioners for the solution to FE coupled consolidation equations, J. Comput. Phys., 227(23) (2008), 9885-9897] is combined with the parallel FSAI preconditioner which is used here to approximate the inverses of both the structural (1, 1) block and an appropriate Schur complement matrix. The resulting preconditioner proves effective in the acceleration of the BiCGSTAB iterative solver. Numerical results on a number of test cases of size up to 2×10⁶ unknowns and 1.2×10⁸ nonzeros show the perfect scalability of the overall code up to 256 processors.     

On a coupled finite element-finite volume method for convection-diffusion problems

In this paper we present and analyse a coupled finite element-finitevolume method for the numerical approximation of singularlyperturbed convection-diffusion problems. The idea is to couplea discretization for the convective term, based on the finitevolume (node-centred) method, and a standard continuous finiteelement approximation of the diffusive term. Such a method preservesconservation, fulfils consistence and enhances stability.     

On structure and open problems in topological theories coupled to topological gravity

The structure of topological theory coupled to topological gravity is studied. We show that in this theoryQ-exact terms do not decouple. This nondecoupling in the action of the theory is connected with the existence of boundaries of the moduli space and leads to problems in defining the topological gravity for massive topological theories. Nondecoupling ofQ-exact observables leads to filtration of the gravitational descendants constructed from matter fields. Two a priori different preferred splittings of this filtration are constructed (one connected with the massive deformation of the theory and the other connected with the flatness of the connection on the space of theories). It is conjectured that they coincide.Institute of Theoretical and Experimental Physics, Bol. Cheremushkinskaya 25, 117259, Moscow, Russia. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 1, pp. 104–112, July, 1994.     

On the convergence of the Galerkin method for coupled thermoelasticity problems

The Cauchy problem for a system of two operator-differential equations is considered that is an abstract statement of linear coupled thermoelasticity problems. Error estimates in the energy norm for the semidiscrete Galerkin method as applied to the Cauchy problem are established without imposing any special conditions on the projection subspaces. By way of illustration, the error estimates are applied to finite element schemes for solving the coupled problem of plate thermoelasticity considered within the framework of the Kirchhoff linearized theory. The results obtained are also applicable to the case when the projection subspaces in the Galerkin method (for the original abstract problem) are the eigenspaces of operators similar to unbounded self-adjoint positive definite operator coefficients of the original equations.     

Elasticity problems involving coupled half-planes

A general method is proposed for reducing problems concerning cracks, cuts, inclusions and interacting blocks in coupled half-planes to complex integral equations, both singular and hyper-singular. The method is based on the fact that if the Kolosov-Muskhelishvili functions are known for a whole plane, then the corresponding functions for coupled half-planes are obtained from them by simple transformations. Boundary integral equations (BIE) are presented, as well as fundamental solutions for isolated forces and periodic systems of forces, which may be used to construct new complex BIEs.     

Boundary element formulation for nonlinear applications in geomechanics

Several types of nonlinearities are considered, using the boundary element method, with emphasis on geomechanical applications. Numerical algorithms to model ‘no-tension’ plastic, viscoplastic and viscoelastic responses are presented. Extension of the method to two-dimensional piecewise homogeneous problems is shown.The overlay technique is adapted for the boundary element formulation to model complex plastic and viscoplastic responses. In particular, the technique is shown to be extremely useful to model time-dependent behaviour. It has also proved suitable for the Bauschinger-effect representation in elastoplastic analysis.Tunnel examples are presented and are shown to be very well suited to solution by boundary elements. The method deals with infinite domains without requiring the definition of an artificial outer boundary. As a result little discretization is needed.     

Spectral analysis of coupled linear complementarity problems

This note deals with the so-called cone-constrained bivariate eigenvalue problem. The equilibrium model under consideration is a system of linear complementarity problems

     

Regions of prevalence in the coupled restricted three-body problems approximation

This work concerns the role played by a couple of the planar circular restricted three-body problem in the approximation of the bicircular model. The comparison between the differential equations governing the dynamics leads to the definition of region of prevalence where one restricted model provides the best approximation of the four-body model. According to this prevalence, the patched three-body problem approximation is used to design first guess trajectories for a spacecraft travelling under the Sun-Earth-Moon gravitational influence.     

On the ellipticity of coupled finite element and one-equation boundary element methods for boundary value problems

In this paper we extend some recent results on the stability of the Johnson–Nédelec coupling of finite and boundary element methods in the case of boundary value problems. In Of and Steinbach (Z Angew Math Mech 93:476–484, 2013), Sayas (SIAM J Numer Anal 47:3451–3463, 2009) and Steinbach (SIAM J Numer Anal 49:1521–1531, 2011), the case of a free-space transmission problem was considered, and sufficient and necessary conditions are stated which ensure the ellipticity of the bilinear form for the coupled problem. The proof was based on considering the energies which are related to both the interior and exterior problem. In the case of boundary value problems for either interior or exterior problems, additional estimates are required to bound the energy for the solutions of related subproblems. Moreover, several techniques for the stabilization of the coupled formulations are analysed. Applications involve boundary value problems with either hard or soft inclusions, exterior boundary value problems, and macro-element techniques.     

Error estimates for discretizations of coupled electromagnetic-mechanical problems

In this note, a method is outlined to obtain a priori error estimates for the finite element discretization of coupled electromagnetic mechanical problems as arise, e.g., in electromagnetic metal forming. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Control problems for weakly coupled systems with memory

We investigate control problems for wave–Petrovsky coupled systems in the presence of memory terms. By writing the solutions as Fourier series, we are able to prove Ingham type estimates, and hence reachability results. Our findings have applications in viscoelasticity theory and linear acoustic theory.     

A coupled NMM-SPH method for fluid-structure interaction problems

The main challenges in the numerical simulation of fluid–structure interaction (FSI) problems include the solid fracture, the free surface fluid flow, and the interactions between the solid and the fluid. Aiming to improve the treatment of these issues, a new coupled scheme is developed in this paper. For the solid structure, the Numerical Manifold Method (NMM) is adopted, in which the solid is allowed to change from continuum to discontinuum. The Smoothed Particle Hydrodynamics (SPH) method, which is suitable for free interface flow problem, is used to model the motion of fluids. A contact algorithm is then developed to handle the interaction between NMM elements and SPH particles. Three numerical examples are tested to validate the coupled NMM-SPH method, including the hydrostatic pressure test, dam-break simulation and crack propagation of a gravity dam under hydraulic pressure. Numerical modeling results indicate that the coupled NMM-SPH method can not only simulate the interaction of the solid structure and the fluid as in conventional methods, but also can predict the failure of the solid structure.     

Constructing eigenfunctions of non-selfadjoint coupled parabolic boundary problems

This paper deals with the eigenfunction construction of coupled parabolic boundary value problems under a more general situation than in previous papers where a certain matrix related to the boundary conditions must have real eigenvalues.     

Quasilinearization method for coupled dynamic problems of thermoviscoelasticity

Use of the quasilinearization method is proposed for the solution of coupled dynamic (particularly, quasistatic) problems of thermoviscoelasticity under cyclic loading. The coupled problems under consideration here include vibrations of a one-dimensional body (beam, plate, shell) and shear vibrations of a hollow cylinder made of a material with temperature-dependent properties, with the principle of temperature-time analogy applicable in the latter case. The quasilinearization method is shown to be a fast converging one when applied to the solution of these problems.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 2, pp. 310–316, March–April, 1976.     

On MAC schemes on triangular delaunay meshes,their convergence and application to coupled flow problems

We study the convergence of two generalized marker‐and‐cell covolume schemes for the incompressible Stokes and Navier–Stokes equations introduced by Cavendish, Hall, Nicolaides, and Porsching. The schemes are defined on unstructured triangular Delaunay meshes and exploit the Delaunay–Voronoi duality. The study is motivated by the fact that the related discrete incompressibility condition allows to obtain a discrete maximum principle for the finite volume solution of an advection–diffusion problem coupled to the flow. The convergence theory uses discrete functional analysis and compactness arguments based on recent results for finite volume discretizations for the biharmonic equation. For both schemes, we prove the strong convergence in L² for the velocities and the discrete rotations of the velocities for the Stokes and the Navier–Stokes problem. Further, for one of the schemes, we also prove the strong convergence of the pressure in L². These predictions are confirmed by numerical examples presented in the article. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1397–1424, 2014     

A coupled far-field formulation for time-periodic numerical problems in fluid dynamics

Consider uniform flow past an oscillating body generating a time-periodic motion in an exterior domain, modelled by a numerical fluid dynamics solver in the near field around the body. A far-field formulation, based on the Oseen equations, is presented for coupling onto this domain thereby enabling the whole space to be modelled. In particular, examples for formulations by boundary elements and infinite elements are described.