Nonsmooth problems formulations and available solvers

Nonsmooth problems formulations and available solvers#

The core of a Siconos simulation consists in writing a formulation for a given problem and choose a solver to determine the unknowns.

The different problems and their features are described below, with the available solvers for each formulation.

Write and solve a problem with Siconos#

Create a problem#

Create and describe a solver#

Solver parameters are handled by the object SolverOptions. It defines which solver will be used, its parameters, like tolerance, possibly handles some internal work arrays or data.

The simplest way to create and use a solver is to select the corresponding id (check the list of avalaible solver for each problem and the corresponding numbers in the pages below) and initialize the solver with this id.

Kernel (high-level) interface:

// -- C++ API --
// use solver id as a parameter for the one-step nonsmooth problem constructor
SP::OneStepNSProblem problem(new LCP(SICONOS_LCP_LEMKE));
// get options :
SP::SolverOptions options = problem->numericsSolverOptions()

// -- Python API --
import siconos.kernel as sk
lcp = sk.LCP(sk.SICONOS_LCP_LEMKE)

Numerics (low-level) interface:

// -- C/C++ API --
int id = SICONOS_LCP_LEMKE;
SolverOptions * options = solver_options_create(id);

// -- Python API --
import siconos.numerics as sn
options = sn.SolverOptions(sn.SICONOS_LCP_LEMKE)

In any case, the id is the only required input. All the other parameters have default values.

To change/update these default values explicitely set the content of iparam or dparam or use solver_options_update_internal() to deal with internal solvers.

e.g.:

// -- C/C++ API --
options->dparam[SICONOS_DPARAM_TOL] = 1e-12;

// Set the first internal solver of options to :enumerative:`SICONOS_FRICTION_3D_NSN_AC`
// and change internal solver maximum number of iterations
int internal_solver_number = 0;
// Reset the internal solver to SICONOS_FRICTION_3D_NSN_AC with default values for its parameters ...
solver_options_update_internal(options, internal_solver_number, SICONOS_FRICTION_3D_NSN_AC);
// and modify the max number of iterations.
options->internalSolvers[internal_solver_number].iparam[SICONOS_IPARAM_MAX_ITER] = 1000;

// -- Python API --
options.dparam[sn.SICONOS_DPARAM_TOL] = 1e-12;
options.update_internal(0, sn.SICONOS_FRICTION_3D_NSN_AC);
options.internalSolvers[0].iparam[sn.SICONOS_IPARAM_MAX_ITER] = 1000

  • an id (int) that uniquely identifies the solver,

  • iparam, an array used to save integer type parameters,

  • dparam, an array used to save real (double) type parameters,

  • internalSolvers : array of SolverOptions used to describe (optional) internal solvers

dparam indices common to all solvers#

  • dparam[SICONOS_DPARAM_TOL] (in): solver tolerance

  • dparam[SICONOS_DPARAM_RESIDU] (out): computed error

iparam indices common to all solvers#

  • iparam[SICONOS_IPARAM_MAX_ITER] (in): maximum number of iterations allowed

  • iparam[SICONOS_IPARAM_PREALLOC] (in): keep work space across calls (?), 0 (false) by default.

  • iparam[SICONOS_IPARAM_ITER_DONE] (out): number of iterations done

Solve a problem#

Numerics (low-level) interface:

// -- C/C++ API --

// Create the solver
int id = SICONOS_LCP_LEMKE;
SolverOptions * options = solver_options_create(id);

// Call the driver
lcp_lexicolemke(problem, z, w, info, options);

// Clear memory
solver_options_delete(&options);

// -- Python API --
import siconos.numerics as sn
options = sn.SolverOptions(sn.SICONOS_LCP_LEMKE)
// ...
sn.lcp_lexicolemke(problem, z, w, info, options)
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