Nonlinear local solver

Scientific Conference (2022, August)

Many engineering applications require solution of a global finite element problem coupled with nonlinear equations of local nature. Local in the sense, that for a known global state the local solution ... [more ▼]

Many engineering applications require solution of a global finite element problem coupled with nonlinear equations of local nature. Local in the sense, that for a known global state the local solution could be found on cell-by-cell basis. Examples include plastic deformation problems, static condensation (hybridization) of displacement-stress formulation or just a simple nonlinear constitutive laws to be satisfied at each quadrature point. These types of problems either required special libraries and extensions in order to be solved with FEniCS (and FEniCS-X) tools, or lead to very slow implementations due to hacks and tricks needed to achieve the solution (e.g. monolithic schemes which increase the matrix problem size). In this talk a unified approach tailored for the current state of FEniCS-X interfaces is presented. The approach computes consistent global tangent operator for nonlinear problems. In addition, local equations are formulated symbolically in UFL, and their derivatives are therefore computed automatically. Several low-level examples (incl. plasticity with symbolic yield surface, nonlinear static condensation and materials with implicit constitutive laws) that demonstrate the main concepts are presented. Finally, high-level wrappers for this functionality are presented. These come as a part of package `dolfiny` (https://github.com/michalhabera/dolfiny). [less ▲]

dolfiny: Convenience wrappers for DOLFINx

Scientific Conference (2021, March 23)

With the increased flexibility of DOLFINx and its reduction to core functionality, the responsibility for even some basic components of computational analysis is shifted to the user. This presentation ... [more ▼]

With the increased flexibility of DOLFINx and its reduction to core functionality, the responsibility for even some basic components of computational analysis is shifted to the user. This presentation provides an overview of the open-source package dolfiny, which provides end-user API interfaces to mesh/meshtags generation and processing, expression list handling, function interpolation and projection as well as the restriction of function spaces to parts of the computational domain. This functionality is consistently considered in interfaces to PETSc/SNES as nonlinear solver and SLEPc as eigensolver backend, both allowing the operation on block and nested operators. In addition, the package provides a convenient approach to incorporate time integration into the UFL formulation of the problem, which is exemplified for the generalised alpha method. The capability of dolfiny is demonstrated in a number of examples, ranging between finite strain structural analysis, plasticity and fluid-structure interaction. [less ▲]