The flecsolve package is a parallel computational framework for multi-physics application development using the open source FleCSI programming system. Flecsolve employs design principles from the AMP package to provide a lightweight set of tools for composing multi-physics applications in FleCSI. Specifically, flecsolve provides a linear algebra interface to the FleCSI data abstraction. This interface is used to implement a set of time integrators and solvers for FleCSI applications.

Library Structure

Components in flecsolve are organized into the following categories:

vectors : Definition of core vector type and specialization of this type for vectors using FleCSI data and vectors with multiple components.

operators : Definition of core operator type used as interface for solvers and time integrators.

matrices : Implementation of various sequential sparse matrix types and a parallel Compressed Sparse Row (CSR) matrix.

solvers : Collection of sparse linear solvers.

time-integrators : Collection of variable step explicit and implicit integrators.

Linear Algebra Interface

The core vector type provides a vector interface using composition of three types:

• Data: interface to the storage
• Operations: implementation of common vector operations
• Variable: static tag to identify a physics field

vec::topo_view specializes this type to adapt user fields defined on a FleCSI topology to the vector interface. The data interface for this vector implementation stores stores a field reference and provides interfaces to the topology instance, accessor types, and index space for the field. The operations type executes FleCSI tasks to implement common vector operations using the vector data.

vec::multi implements the vector interface for a collection of component vectors. This enables a natural grouping of physics components and permits operators to select a subset of the multivector on which to operate.

Operators in flecsolve fundamentally define a map from a domain vector to a range vector. This map is given by defining a type with an apply function and implementing the desired map through FleCSI task execution or the provided vector operations. Optionally, input and output variables may be specified to indicate a subset of the physics on which to operate. A flecsolve operator is then constructed through specialization of op::core with this type.

Krylov solvers and time integrators provided by flecsolve are implemented generically using the vector operations and operator interface. This enables them to be used with a variety of FleCSI topologies, automatically deducing the user types when field references are wrapped in vec::topo_view.

Krylov Solvers

Krylov solvers in flecsolve are defined using a collection of types with common names in their respective namespace. These types are then used to construct a flecsolve operator that computes the approximate inverse mapping. These types are summarized below.

settings : Configuration settings for the solver (e.g., tolerances, maximum iteration counts, ...).

options : Specification of boost options_description for Krylov solver and mapping to its settings type. This is used with read_config to populate the settings type dynamically from a config file.

make_work : Given an exemplar vector used for type deduction, creates the appropriate number of work vectors needed during a solve.

solver : Entry point for each Krylov solver containing type information in addition to storing the solver settings and auxiliary work vectors needed during a solve. The appropriate number of work vectors needs to be be provided as FleCSI fields cannot be constructed dynamically during a solve. To solve a given problem, the solver type includes a function call operator that returns an approximate inverse in the form of a flecsolve operator. This function takes handles to operator to invert and optionally a preconditioner and diagnostic function as input.

Operator Handles

Operator handles are used to make ownership explicit when passing flecsolve operators to a solver or time integrator. For shared ownership semantics, a flecsolve operator is constructed using op::make_shared. This returns a handle with shared ownership. For a non-owning reference to an operator, op::ref or op::cref are used to construct an operator handle.

Diagnostic Functions

Users may optionally provide a diagnostic function to a Krylov solver when binding operators to the solver. This allows users to monitor solver convergence and provide an early termination condition. A diagnostic function can be a callable of the following form:

bool diagnostic(const Vector & current_solution, double residual_norm)

The return value is used to indicate early termination based on the inputs.

Release

This software has been approved for open source release and has been assigned O4869.

License

This program is Open-Source under the BSD-3 License.