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DiffEqOperators.jl is a package for finite difference discretization of partial differential equations. It allows building lazy operators for high order non-uniform finite differences in an arbitrary number of dimensions, including vector calculus operators. For the operators, both centered and upwind operators are provided, for domains of any dimension, arbitrarily spaced grids, and for any order of accuracy. The cases of 1, 2, and 3 dimensions with an evenly spaced grid are optimized with a convolution routine from NNlib.jl. Care is taken to give efficiency by avoiding unnecessary allocations, using purpose-built stencil compilers, allowing GPUs and parallelism, etc. Any operator can be concretized as an Array, a BandedMatrix or a sparse matrix.
Features
- Documentation available
- Examples available
- Linear operators for discretizations
- Differential equations and scientific machine learning
- For the operators, both centered and upwind operators are provided
- Care is taken to give efficiency by avoiding unnecessary allocations
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