mcpca / marlin

A parallel solver for first-order static Hamilton-Jacobi PDEs

marlin

A C++14 implementation of a Lax-Friedrichs fast sweeping method for first-order static Hamilton-Jacobi equations.

The implementation is based on the algorithm described in Kao, Osher and Qian, Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations (available here), and is parallelized using the hyperplane stepping method described in Detrixhe, Gibou and Min, A parallel fast sweeping method for the Eikonal equation (link).

It is dimension-agnostic (the dimension is set at compile time).

Building

A C++14 compiler with OpenMP support is required to build the library.

  $ mkdir build && cd build
  $ cmake .. -DCMAKE_BUILD_TYPE=RELEASE
  $ make

Usage

The number of dimensions and the floating value type to use in computations (i.e., float, double or long double) can be set in the header marlin/include/defs.hpp. The dimension can also be set using the macro MARLIN_N_DIMS.

The solver constructor takes four parameters:

• an array of floating point values which contains the values of the right-hand-side of the equation in row major order. Gridoints at which the Dirichlet boundary condition is imposed must have their value inverted in sign and shifted by negative one, e.g., if the boundary condition value is 0 at some point, the corresponding value in the array should be -1;

• an array containing the size of the grid in each dimension;

• the limits of the computational domain as an array of (min, max) pairs;

• the initial value of the solution and the tolerance (the epsilon value for the convergence criterion). These are passed inside a struct to avoid having a constructor which takes more than one argument of the same type, which can lead to errors in the order of arguments.

The Hamiltonian and the viscosity coefficients can be any kind of callable object (function pointers, functors, lambdas, etc).

Check the examples for how to set up and call the solver.

Examples

Four examples are included in the examples directory.

In examples/scripts there are Python scripts which set up the problem, call the solver and display the results. For instance, to run the eikonal3d example:

  $ cd build
  $ make examples
  $ cd ../examples/scripts
  $ mkdir ../data
  $ ./eikonal3d.py

(make examples builds all the examples, so to run subsequent examples all you have to do is call the corresponding script.)

Since the default number of dimensions is 3, you'll have to change the number of dimensions to 2 and recompile in order to run the two-dimensional examples.

You'll need to have numpy and h5py installed to run the examples. The two-dimensional examples also require matplotlib.

Acknowledgments

• LSTS-FEUP
• Jorge Estrela da Silva