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While double\u2010precision arithmetic has traditionally been used to ensure numerical accuracy, there is a growing demand for single\u2010 and mixed\u2010precision calculations as GPU\u2010accelerated MD simulations become increasingly widespread. In this study, we present improvements to the constraint solvers through an analytical treatment for bonds involving a single hydrogen atom ( groups). For more complex groups with multiple hydrogens ( and ), we introduce two precision\u2010level implementation strategies: (1) a mixed\u2010precision approach, where variables are generally described in single\u2010precision while temporary coordinate updates are handled in double\u2010precision and (2) a pairwise arithmetic approach, where temporary coordinate variables are represented as pairs of single\u2010precision values to reduce rounding errors. These implementation strategies reduce velocity\u2010update errors compared with schemes using single precision for all variables. Energy drift analysis in microcanonical simulations confirms that these strategies maintain accuracy comparable to full double\u2010precision implementations. Performance benchmarks on GPUs with limited FP64 throughput (RTX 3080 and A6000 Ada) show that our proposed implementation strategies substantially reduce runtime compared with full double\u2010precision calculations. Conversely, on architectures with balanced FP32 and FP64 performance, such as CPUs or H100 GPUs, full double\u2010precision arithmetic remains the preferred choice for the constraint kernels evaluated in this study. Overall, these findings demonstrate that the proposed strategies provide an effective balance between numerical accuracy and computational performance on GPUs with limited FP64 throughput.<\/jats:p>","DOI":"10.1002\/jcc.70492","type":"journal-article","created":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T05:55:29Z","timestamp":1789710929000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimized M\u2010\n                    <scp>SHAKE<\/scp>\n                    Constraint Implementations for\n                    <scp>GPU<\/scp>\n                    \u2010Accelerated Molecular Dynamics: Balancing Precision and Performance Across Architectures"],"prefix":"10.1002","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2285-4432","authenticated-orcid":false,"given":"Jaewoon","family":"Jung","sequence":"first","affiliation":[{"name":"Computational Biophysics Team RIKEN Center for Computational 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Institute of Technology  Saitama Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9738-9216","authenticated-orcid":false,"given":"Yuji","family":"Sugita","sequence":"additional","affiliation":[{"name":"Computational Biophysics Team RIKEN Center for Computational Science  Kobe Japan"},{"name":"Theoretical Molecular Science Laboratory RIKEN Pioneering Research Institute  Wako Japan"},{"name":"Department of Physics University of Tokyo  Tokyo 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