7.3. Code Organization
7.3.1. IDAS organization
The IDAS package is written in ANSI C. The following summarizes the basic structure of the package, although knowledge of this structure is not necessary for its use.
The overall organization of the IDAS package is shown in
Fig. 7.4. IDAS utilizes generic linear and nonlinear
solvers defined by the
SUNLinearSolver (see §11) and
SUNNonlinearSolver interfaces (see §12) respectively. As
such, IDAS has no knowledge of the method being used to solve the linear and
nonlinear systems that arise. For any given user problem, there exists a single
nonlinear solver interface and, if necessary, one of the linear system solver
interfaces is specified, and invoked as needed during the integration.
IDAS has a single unified linear solver interface, IDALS, supporting both direct
and iterative linear solvers built using the generic
interface (see §11). These solvers may utilize a
object (see §10) for storing Jacobian information, or they may
be matrix-free. Since IDAS can operate on any valid
SUNLinearSolver, the set
of linear solver modules available to IDAS will expand as new
implementations are developed.
For users employing SUNMATRIX_DENSE or SUNMATRIX_BAND Jacobian matrices, IDAS includes algorithms for their approximation through difference quotients, although the user also has the option of supplying a routine to compute the Jacobian (or an approximation to it) directly. This user-supplied routine is required when using sparse or user-supplied Jacobian matrices.
For users employing matrix-free iterative linear solvers, IDAS includes an algorithm for the approximation by difference quotients of the product \(Jv\). Again, the user has the option of providing routines for this operation, in two phases: setup (preprocessing of Jacobian data) and multiplication.
For preconditioned iterative methods, the preconditioning must be supplied by the user, again in two phases: setup and solve. While there is no default choice of preconditioner analogous to the difference-quotient approximation in the direct case, the references [22, 27], together with the example and demonstration programs included with IDAS, offer considerable assistance in building preconditioners.
IDA’s linear solver interface consists of four primary phases, devoted to (1) memory allocation and initialization, (2) setup of the matrix data involved, (3) solution of the system, and (4) freeing of memory. The setup and solution phases are separate because the evaluation of Jacobians and preconditioners is done only periodically during the integration, and only as required to achieve convergence. The call list within the central IDAS module to each of the four associated functions is fixed, thus allowing the central module to be completely independent of the linear system method.
IDAS also provides a preconditioner module, for use with any of the Krylov iterative linear solvers. It works in conjunction with the NVECTOR_PARALLEL and generates a preconditioner that is a block-diagonal matrix with each block being a banded matrix.
All state information used by IDAS to solve a given problem is stored in
N_Vector instances. There is no global data in the IDAS package, and so, in
this respect, it is reentrant. State information specific to the linear and
nonlinear solver are saved in the
instances respectively. The reentrancy of IDAS enables the setting where two or
more problems are solved by intermixed or parallel calls to different instances
of the package from within a single user program.