What question did this study set out to answer?

To introduce and evaluate Lineal, a C++20 linear algebra library designed to optimize memory consumption and runtime when solving large sparse linear systems arising from PDE discretization.

August 16, 2026GEM - International Journal on GeomathematicsOpen Access

Lineal: An efficient linear algebra library

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Authors

KBKurt BöhmClausthal University of Technology OIOlaf IppischClausthal University of Technology

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Implication

Computational evaluation demonstrates reduced memory and runtime using Lineal's hybrid algebraic multigrid for PDE discretization, highlighting scalable sparse solvers on standard hardware.

Key Points

To introduce and evaluate Lineal, a C++20 linear algebra library designed to optimize memory consumption and runtime when solving large sparse linear systems arising from PDE discretization.
Designed a hybrid Algebraic Multi-Grid solver (MAMGO) employing matrix-free stencil representations on the finest grid level alongside Compressed Sparse Row (CSR) matrices on coarser levels.
Integrated flexible mixed precision, multithreading, explicit SIMD instructions, and cache tiling.
Benchmarked performance against hypre (BoomerAMG), DUNE ISTL, and Ginkgo on 3D stationary diffusion problems across soil sample scans and the SPE10 Model 2 benchmark.
On the baseline dataset, Lineal required less than half the runtime and memory of hypre, DUNE ISTL, and Ginkgo when using CSR matrices, and less than one quarter using the hybrid matrix-free solver.
Lineal was the only evaluated library capable of solving the larger high-resolution soil dataset on the test system due to its reduced memory footprint.

Cite This Study

Böhm et al. (2026) studied this question.

synapsesocial.com/papers/6a8178fcf2fb91fc834ac277 https://doi.org/10.1007/s13137-026-00284-9

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Implication

Computational evaluation demonstrates reduced memory and runtime using Lineal's hybrid algebraic multigrid for PDE discretization, highlighting scalable sparse solvers on standard hardware.