The lymph 2.0 library: p-adaptive algorithms and parallel assembly strategies for polytopal DG methods
Keywords
Advanced Numerical Methods for Scientific Computing
Code:
54/2026
Title:
The lymph 2.0 library: p-adaptive algorithms and parallel assembly strategies for polytopal DG methods
Date:
Tuesday 23rd June 2026
Author(s):
Antonietti, P. F.; Corti, M.; Leimer Saglio, C. B.; Pagani, S.
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Abstract:
This work presents a new release of the lymph 2.0 library \cite{antonietti_lymph_2025}, 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.