The lymph 2.0 library: p-adaptive algorithms and parallel assembly strategies for polytopal DG methods
For researchers using high-order DG methods, this library provides p-adaptivity and parallel assembly, but the improvements are incremental.
The lymph 2.0 library extends its support for p-adaptive discontinuous Galerkin methods on polytopal meshes and introduces a unified assembly framework for parallel computation, reducing computational cost while preserving accuracy.
This work presents a new release of the lymph 2.0 library, an open-source MATLAB framework for high-order discontinuous Galerkin discretizations on general polytopal meshes. The lymph 2.0 version is extended to support discretizations with element-wise polynomial approximation degrees, which allows the design of $p$-adaptive strategies based on a posteriori error indicators. In addition, the library introduces a unified assembly framework that abstracts the construction of discrete operators from the underlying physical model, improving code modularity, parallelism, maintainability, and extensibility. Moreover, the proposed approach enables shared-memory parallelism through dedicated parallel tools. Several numerical examples demonstrate the effectiveness of the proposed developments in reducing the computational cost while preserving approximation accuracy.