With the rapid increase of the transistor number in VLSI, rapidly rising power density and temperatures make heat dissipation a major challenge in IC design and manufacturing. However, conventional deterministic thermal analysis methods have difficulties in obtaining local temperature solutions efficiently, and the existing stochastic method is inaccurate when dealing with thermal analysis problems involving Robin boundary conditions (BCs). In this article, a highly parallelized path integral random walk (PIRW) solver is innovatively proposed for steady-state thermal analysis with mixed BCs, especially Robin BCs. The rigorous calculation of the local time and the Feynman-Kac functional$\hat {e}_{c}(t)$are adopted to accurately handle Neumann and Robin BCs for the first time. Furthermore, based on the PIRW, we propose an accurate and microsecond-level precalculation PIRW (pPIRW) predictor, which precalculates time-consuming random walks, obtains temperatures by simple vector multiplication, and therefore is suitable for proactive thermal management. The pPIRW essentially calculates a partial inverse of large-scale matrices constructed from the finite difference-based compact thermal models (CTMs). Experimental results show that compared with 3D-ICE, the PIRW solver maintains high accuracy with a negligible error within$0.5~^{\circ }$C, achieves$136\times $–$209\times $speedup and$8.53\times $–$11.1\times $storage space reduction with all three kinds of BCs, and decreases to$1\times $–$1.53\times $speedup for lacking the absorbing Dirichlet boundary. The pPIRW further has speed improvement of 2.5e$4\times $–6.7e$6\times $and memory reduction of$36.6\times $–$42.5\times $over PIRW without loss of accuracy. Integrated within a thermal management strategy, the pPIRW predictor can eliminate all thermal conflicts while maintaining the highest working frequency. Meanwhile, pPIRW achieves$29.2\times $speedup and$634\times $memory reduction over the CTM during the offline precalculation stage.

In this work, we propose a path integral random walk (PIRW) solver, the first accurate stochastic method for steady-state thermal analysis with mixed boundary conditions, especially involving Fourier heat transfer Robin boundary conditions. We innovatively adopt the strictly correct calculation of the local time and the Feynman-Kac functional êc (t) to handle Neumann and Robin boundary conditions with high precision. Compared with ANSYS, experimental results show that PIRW achieves over 121× speedup and over 83× storage space reduction with a negligible error within 0.8° C at a single point. An application combining PIRW with low-accuracy ANSYS for the temperature calculation at hot-spots is provided as a more accurate and faster solution than only ANSYS used.

SUMMARY: A new version (version 2) of the genomic dose-response analysis software, BMDExpress, has been created. The software addresses the increasing use of transcriptomic dose-response data in toxicology, drug design, risk assessment and translational research. In this new version, we have implemented additional statistical filtering options (e.g. Williams' trend test), curve fitting models, Linux and Macintosh compatibility and support for additional transcriptomic platforms with up-to-date gene annotations. Furthermore, we have implemented extensive data visualizations, on-the-fly data filtering, and a batch-wise analysis workflow. We have also significantly re-engineered the code base to reflect contemporary software engineering practices and streamline future development. The first version of BMDExpress was developed in 2007 to meet an unmet demand for easy-to-use transcriptomic dose-response analysis software. Since its original release, however, transcriptomic platforms, technologies, pathway annotations and quantitative methods for data analysis have undergone a large change necessitating a significant re-development of BMDExpress. To that end, as of 2016, the National Toxicology Program assumed stewardship of BMDExpress. The result is a modernized and updated BMDExpress 2 that addresses the needs of the growing toxicogenomics user community. AVAILABILITY AND IMPLEMENTATION: BMDExpress 2 is available at https://github.com/auerbachs/BMDExpress-2/releases. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.