[1] Solver coupling can extend the capability of existing modeling software and provide a new venue to address previously intractable problems. A software package has been developed to couple geophysical solvers, demonstrating a method to accurately and efficiently solve multiscale geophysical problems with reengineered software using a computational framework (Pyre). Pyre is a modeling framework capable of handling all aspects of the specification and launching of numerical investigations. We restructured and ported CitcomS, a finite element code for mantle convection, into the Pyre framework. Two CitcomS solvers are coupled to investigate the interaction of a plume at high resolution with global mantle flow at low resolution. A comparison of the coupled models with parameterized models demonstrates the accuracy and efficiency of the coupled models and illustrates the limitations and utility of parameterized models.

This paper is concerned with the formulation of a variational r-adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configuration forces for isoparametric elements and nonlinear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and nonlinear elastic bodies; and the optimization of the shape of elastic inclusions.

SUMMARYWe develop and analyse a composite 'CT3D' tetrahedral element consisting of an ensemble of 12 four-node linear tetrahedral elements, coupled to a linear assumed deformation deÿned over the entire domain of the composite element. The element is designed to have well-deÿned lumped masses and contact tractions in dynamic contact problems while at the same time, minimizing the number of volume constraints per element. The relation between displacements and deformations is enforced weakly by recourse to the Hu-Washizu principle. The element arrays are formulated in accordance with the 'assumed-strain' prescription. The formulation of the element accounts for fully non-linear kinematics. Integrals over the domain of the element are computed by a ÿve-point quadrature rule. The element passes the patch test in arbitrarily distorted conÿgurations. Our numerical tests demonstrate that CT element has been found to possess a convergence rate comparable to those of linear simplicial elements, and that these convergence rates are maintained as the near-incompressible limit is approached. We have also veriÿed that the element satisÿes the BabuÄ ska-Brezzi condition for a regular mesh conÿgu-ration. These tests suggest that the CT3D element can indeed be used reliably in calculations involving near-incompressible behaviour which arises, e.g., in the presence of unconÿned plastic ow.

No abstract