Efficient implementation of Galerkin meshfree methods for large-scale problems with an emphasis on maximum entropy approximants

• We propose a simple method to implement matrix assembly in Galerkin meshfree methods.
• By looping over groups of quadrature points, performance is significantly improved.
• We propose a method to efficiently store the maximum entropy basis functions.
• It stores partial information, at the expense of a negligible amount of extra operations.

In Galerkin meshfree methods, because of a denser and unstructured connectivity, the creation and assembly of sparse matrices is expensive. Additionally, the cost of computing basis functions can be significant in problems requiring repetitive evaluations. We show that it is possible to overcome these two bottlenecks resorting to simple and effective algorithms. First, we create and fill the matrix by coarse-graining the connectivity between quadrature points and nodes. Second, we store only partial information about the basis functions, striking a balance between storage and computation. We show the performance of these strategies in relevant problems.