[{"external_id":{"arxiv":["1703.02456"]},"title":"A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices","department":[{"_id":"27"},{"_id":"518"},{"_id":"304"},{"_id":"104"}],"project":[{"_id":"32","name":"Performance and Efficiency in HPC with Custom Computing","grant_number":"PL 595/2-1 / 320898746"},{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"date_updated":"2023-09-26T11:45:02Z","doi":"10.4208/cicp.OA-2018-0053","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We address the general mathematical problem of computing the inverse p-th\r\nroot of a given matrix in an efficient way. A new method to construct iteration\r\nfunctions that allow calculating arbitrary p-th roots and their inverses of\r\nsymmetric positive definite matrices is presented. We show that the order of\r\nconvergence is at least quadratic and that adaptively adjusting a parameter q\r\nalways leads to an even faster convergence. In this way, a better performance\r\nthan with previously known iteration schemes is achieved. The efficiency of the\r\niterative functions is demonstrated for various matrices with different\r\ndensities, condition numbers and spectral radii."}],"user_id":"15278","publisher":"Global Science Press","quality_controlled":"1","author":[{"last_name":"Richters","full_name":"Richters, Dorothee","first_name":"Dorothee"},{"last_name":"Lass","id":"24135","first_name":"Michael","orcid":"0000-0002-5708-7632","full_name":"Lass, Michael"},{"first_name":"Andrea","full_name":"Walther, Andrea","last_name":"Walther"},{"orcid":"0000-0001-5728-9982","full_name":"Plessl, Christian","first_name":"Christian","id":"16153","last_name":"Plessl"},{"last_name":"Kühne","id":"49079","first_name":"Thomas","full_name":"Kühne, Thomas"}],"publication":"Communications in Computational Physics","status":"public","date_created":"2017-07-25T14:48:26Z","volume":25,"_id":"21","intvolume":" 25","issue":"2","year":"2019","type":"journal_article","citation":{"ieee":"D. Richters, M. Lass, A. Walther, C. Plessl, and T. Kühne, “A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices,” Communications in Computational Physics, vol. 25, no. 2, pp. 564–585, 2019, doi: 10.4208/cicp.OA-2018-0053.","short":"D. Richters, M. Lass, A. Walther, C. Plessl, T. Kühne, Communications in Computational Physics 25 (2019) 564–585.","mla":"Richters, Dorothee, et al. “A General Algorithm to Calculate the Inverse Principal P-Th Root of Symmetric Positive Definite Matrices.” Communications in Computational Physics, vol. 25, no. 2, Global Science Press, 2019, pp. 564–85, doi:10.4208/cicp.OA-2018-0053.","bibtex":"@article{Richters_Lass_Walther_Plessl_Kühne_2019, title={A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices}, volume={25}, DOI={10.4208/cicp.OA-2018-0053}, number={2}, journal={Communications in Computational Physics}, publisher={Global Science Press}, author={Richters, Dorothee and Lass, Michael and Walther, Andrea and Plessl, Christian and Kühne, Thomas}, year={2019}, pages={564–585} }","chicago":"Richters, Dorothee, Michael Lass, Andrea Walther, Christian Plessl, and Thomas Kühne. “A General Algorithm to Calculate the Inverse Principal P-Th Root of Symmetric Positive Definite Matrices.” Communications in Computational Physics 25, no. 2 (2019): 564–85. https://doi.org/10.4208/cicp.OA-2018-0053.","ama":"Richters D, Lass M, Walther A, Plessl C, Kühne T. A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices. Communications in Computational Physics. 2019;25(2):564-585. doi:10.4208/cicp.OA-2018-0053","apa":"Richters, D., Lass, M., Walther, A., Plessl, C., & Kühne, T. (2019). A General Algorithm to Calculate the Inverse Principal p-th Root of Symmetric Positive Definite Matrices. Communications in Computational Physics, 25(2), 564–585. https://doi.org/10.4208/cicp.OA-2018-0053"},"page":"564-585"},{"file":[{"creator":"plessl","file_id":"12872","file_size":248360,"relation":"main_file","content_type":"application/pdf","date_updated":"2019-07-22T12:45:02Z","date_created":"2019-07-22T12:45:02Z","file_name":"plessl19_informatik_spektrum.pdf","access_level":"open_access"}],"author":[{"full_name":"Platzner, Marco","first_name":"Marco","id":"398","last_name":"Platzner"},{"orcid":"0000-0001-5728-9982","full_name":"Plessl, Christian","first_name":"Christian","id":"16153","last_name":"Plessl"}],"quality_controlled":"1","publication":"Informatik Spektrum","file_date_updated":"2019-07-22T12:45:02Z","status":"public","has_accepted_license":"1","date_created":"2019-07-22T12:42:44Z","user_id":"15278","ddc":["004"],"year":"2019","citation":{"ieee":"M. Platzner and C. Plessl, “FPGAs im Rechenzentrum,” Informatik Spektrum, 2019, doi: 10.1007/s00287-019-01187-w.","short":"M. Platzner, C. Plessl, Informatik Spektrum (2019).","mla":"Platzner, Marco, and Christian Plessl. “FPGAs im Rechenzentrum.” Informatik Spektrum, 2019, doi:10.1007/s00287-019-01187-w.","bibtex":"@article{Platzner_Plessl_2019, title={FPGAs im Rechenzentrum}, DOI={10.1007/s00287-019-01187-w}, journal={Informatik Spektrum}, author={Platzner, Marco and Plessl, Christian}, year={2019} }","chicago":"Platzner, Marco, and Christian Plessl. “FPGAs im Rechenzentrum.” Informatik Spektrum, 2019. https://doi.org/10.1007/s00287-019-01187-w.","apa":"Platzner, M., & Plessl, C. (2019). FPGAs im Rechenzentrum. Informatik Spektrum. https://doi.org/10.1007/s00287-019-01187-w","ama":"Platzner M, Plessl C. FPGAs im Rechenzentrum. Informatik Spektrum. Published online 2019. doi:10.1007/s00287-019-01187-w"},"type":"journal_article","_id":"12871","department":[{"_id":"27"},{"_id":"518"},{"_id":"78"}],"publication_identifier":{"issn":["0170-6012","1432-122X"]},"publication_status":"published","title":"FPGAs im Rechenzentrum","language":[{"iso":"ger"}],"date_updated":"2023-09-26T11:45:57Z","oa":"1","doi":"10.1007/s00287-019-01187-w"},{"issue":"2","_id":"20","intvolume":" 10","page":" 33-36","year":"2018","citation":{"short":"M. Lass, T. Kühne, C. Plessl, Embedded Systems Letters 10 (2018) 33–36.","ieee":"M. Lass, T. Kühne, and C. Plessl, “Using Approximate Computing for the Calculation of Inverse Matrix p-th Roots,” Embedded Systems Letters, vol. 10, no. 2, pp. 33–36, 2018.","apa":"Lass, M., Kühne, T., & Plessl, C. (2018). Using Approximate Computing for the Calculation of Inverse Matrix p-th Roots. Embedded Systems Letters, 10(2), 33–36. https://doi.org/10.1109/LES.2017.2760923","ama":"Lass M, Kühne T, Plessl C. Using Approximate Computing for the Calculation of Inverse Matrix p-th Roots. Embedded Systems Letters. 2018;10(2):33-36. doi:10.1109/LES.2017.2760923","chicago":"Lass, Michael, Thomas Kühne, and Christian Plessl. “Using Approximate Computing for the Calculation of Inverse Matrix P-Th Roots.” Embedded Systems Letters 10, no. 2 (2018): 33–36. https://doi.org/10.1109/LES.2017.2760923.","mla":"Lass, Michael, et al. “Using Approximate Computing for the Calculation of Inverse Matrix P-Th Roots.” Embedded Systems Letters, vol. 10, no. 2, IEEE, 2018, pp. 33–36, doi:10.1109/LES.2017.2760923.","bibtex":"@article{Lass_Kühne_Plessl_2018, title={Using Approximate Computing for the Calculation of Inverse Matrix p-th Roots}, volume={10}, DOI={10.1109/LES.2017.2760923}, number={2}, journal={Embedded Systems Letters}, publisher={IEEE}, author={Lass, Michael and Kühne, Thomas and Plessl, Christian}, year={2018}, pages={33–36} }"},"type":"journal_article","user_id":"16153","abstract":[{"lang":"eng","text":"Approximate computing has shown to provide new ways to improve performance\r\nand power consumption of error-resilient applications. While many of these\r\napplications can be found in image processing, data classification or machine\r\nlearning, we demonstrate its suitability to a problem from scientific\r\ncomputing. Utilizing the self-correcting behavior of iterative algorithms, we\r\nshow that approximate computing can be applied to the calculation of inverse\r\nmatrix p-th roots which are required in many applications in scientific\r\ncomputing. Results show great opportunities to reduce the computational effort\r\nand bandwidth required for the execution of the discussed algorithm, especially\r\nwhen targeting special accelerator hardware."}],"volume":10,"date_created":"2017-07-25T14:41:08Z","status":"public","publication":"Embedded Systems Letters","author":[{"last_name":"Lass","id":"24135","first_name":"Michael","full_name":"Lass, Michael","orcid":"0000-0002-5708-7632"},{"id":"49079","last_name":"Kühne","full_name":"Kühne, Thomas","first_name":"Thomas"},{"orcid":"0000-0001-5728-9982","full_name":"Plessl, Christian","first_name":"Christian","id":"16153","last_name":"Plessl"}],"publisher":"IEEE","doi":"10.1109/LES.2017.2760923","date_updated":"2022-01-06T06:54:18Z","language":[{"iso":"eng"}],"title":"Using Approximate Computing for the Calculation of Inverse Matrix p-th Roots","external_id":{"arxiv":["1703.02283"]},"publication_identifier":{"issn":["1943-0663"],"eissn":["1943-0671"]},"publication_status":"published","project":[{"name":"Performance and Efficiency in HPC with Custom Computing","grant_number":"PL 595/2-1","_id":"32"},{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"department":[{"_id":"27"},{"_id":"518"},{"_id":"304"}]},{"status":"public","project":[{"_id":"1","name":"SFB 901"},{"_id":"4","name":"SFB 901 - Project Area C"},{"name":"SFB 901 - Subproject C2","_id":"14"}],"date_created":"2018-11-07T15:14:26Z","publisher":"Universität Paderborn","author":[{"last_name":"Filmwala","first_name":"Tasneem","full_name":"Filmwala, Tasneem"}],"department":[{"_id":"27"},{"_id":"518"}],"title":"Study Effects of Approximation on Conjugate Gradient Algorithm and Accelerate it on FPGA Platform","user_id":"477","year":"2018","citation":{"chicago":"Filmwala, Tasneem. Study Effects of Approximation on Conjugate Gradient Algorithm and Accelerate It on FPGA Platform. Universität Paderborn, 2018.","apa":"Filmwala, T. (2018). Study Effects of Approximation on Conjugate Gradient Algorithm and Accelerate it on FPGA Platform. Universität Paderborn.","ama":"Filmwala T. Study Effects of Approximation on Conjugate Gradient Algorithm and Accelerate It on FPGA Platform. Universität Paderborn; 2018.","bibtex":"@book{Filmwala_2018, title={Study Effects of Approximation on Conjugate Gradient Algorithm and Accelerate it on FPGA Platform}, publisher={Universität Paderborn}, author={Filmwala, Tasneem}, year={2018} }","mla":"Filmwala, Tasneem. Study Effects of Approximation on Conjugate Gradient Algorithm and Accelerate It on FPGA Platform. Universität Paderborn, 2018.","short":"T. Filmwala, Study Effects of Approximation on Conjugate Gradient Algorithm and Accelerate It on FPGA Platform, Universität Paderborn, 2018.","ieee":"T. Filmwala, Study Effects of Approximation on Conjugate Gradient Algorithm and Accelerate it on FPGA Platform. Universität Paderborn, 2018."},"type":"mastersthesis","supervisor":[{"full_name":"Plessl, Christian","orcid":"0000-0001-5728-9982","first_name":"Christian","id":"16153","last_name":"Plessl"}],"language":[{"iso":"eng"}],"date_updated":"2022-01-06T07:01:52Z","_id":"5414"},{"citation":{"apa":"Gadewar, O. (2018). Programmable Programs? - Designing FPGA Overlay Architectures with OpenCL. Universität Paderborn.","ama":"Gadewar O. Programmable Programs? - Designing FPGA Overlay Architectures with OpenCL. Universität Paderborn; 2018.","chicago":"Gadewar, Onkar. Programmable Programs? - Designing FPGA Overlay Architectures with OpenCL. Universität Paderborn, 2018.","mla":"Gadewar, Onkar. Programmable Programs? - Designing FPGA Overlay Architectures with OpenCL. Universität Paderborn, 2018.","bibtex":"@book{Gadewar_2018, title={Programmable Programs? - Designing FPGA Overlay Architectures with OpenCL}, publisher={Universität Paderborn}, author={Gadewar, Onkar}, year={2018} }","short":"O. Gadewar, Programmable Programs? - Designing FPGA Overlay Architectures with OpenCL, Universität Paderborn, 2018.","ieee":"O. Gadewar, Programmable Programs? - Designing FPGA Overlay Architectures with OpenCL. Universität Paderborn, 2018."},"year":"2018","type":"mastersthesis","supervisor":[{"last_name":"Plessl","id":"16153","first_name":"Christian","full_name":"Plessl, Christian","orcid":"0000-0001-5728-9982"}],"language":[{"iso":"eng"}],"_id":"5421","date_updated":"2022-01-06T07:01:53Z","department":[{"_id":"27"},{"_id":"518"}],"author":[{"first_name":"Onkar","full_name":"Gadewar, Onkar","last_name":"Gadewar"}],"publisher":"Universität Paderborn","project":[{"name":"SFB 901","_id":"1"},{"name":"SFB 901 - Project Area C","_id":"4"},{"_id":"14","name":"SFB 901 - Subproject C2"}],"date_created":"2018-11-07T16:16:56Z","status":"public","title":"Programmable Programs? - Designing FPGA Overlay Architectures with OpenCL","user_id":"477"},{"title":"Sprint diagnostic with GPS and inertial sensor fusion","department":[{"_id":"27"},{"_id":"518"}],"publication_status":"published","publication_identifier":{"issn":["1369-7072","1460-2687"]},"date_updated":"2022-01-06T07:03:09Z","doi":"10.1007/s12283-018-0291-0","language":[{"iso":"eng"}],"user_id":"16153","ddc":["000"],"file":[{"content_type":"application/pdf","date_updated":"2019-01-08T17:47:06Z","relation":"main_file","file_size":2141021,"creator":"plessl","file_id":"6517","access_level":"closed","file_name":"plessl18_sportseng.pdf","date_created":"2019-01-08T17:47:06Z"}],"author":[{"first_name":"Jan Cedric","full_name":"Mertens, Jan Cedric","last_name":"Mertens"},{"full_name":"Boschmann, Alexander","first_name":"Alexander","last_name":"Boschmann"},{"first_name":"M.","full_name":"Schmidt, M.","last_name":"Schmidt"},{"id":"16153","last_name":"Plessl","orcid":"0000-0001-5728-9982","full_name":"Plessl, Christian","first_name":"Christian"}],"publisher":"Springer Nature","quality_controlled":"1","publication":"Sports Engineering","file_date_updated":"2019-01-08T17:47:06Z","status":"public","has_accepted_license":"1","date_created":"2019-01-08T17:44:43Z","volume":21,"intvolume":" 21","_id":"6516","issue":"4","type":"journal_article","citation":{"short":"J.C. Mertens, A. Boschmann, M. Schmidt, C. Plessl, Sports Engineering 21 (2018) 441–451.","ieee":"J. C. Mertens, A. Boschmann, M. Schmidt, and C. Plessl, “Sprint diagnostic with GPS and inertial sensor fusion,” Sports Engineering, vol. 21, no. 4, pp. 441–451, 2018.","chicago":"Mertens, Jan Cedric, Alexander Boschmann, M. Schmidt, and Christian Plessl. “Sprint Diagnostic with GPS and Inertial Sensor Fusion.” Sports Engineering 21, no. 4 (2018): 441–51. https://doi.org/10.1007/s12283-018-0291-0.","apa":"Mertens, J. C., Boschmann, A., Schmidt, M., & Plessl, C. (2018). Sprint diagnostic with GPS and inertial sensor fusion. Sports Engineering, 21(4), 441–451. https://doi.org/10.1007/s12283-018-0291-0","ama":"Mertens JC, Boschmann A, Schmidt M, Plessl C. Sprint diagnostic with GPS and inertial sensor fusion. Sports Engineering. 2018;21(4):441-451. doi:10.1007/s12283-018-0291-0","bibtex":"@article{Mertens_Boschmann_Schmidt_Plessl_2018, title={Sprint diagnostic with GPS and inertial sensor fusion}, volume={21}, DOI={10.1007/s12283-018-0291-0}, number={4}, journal={Sports Engineering}, publisher={Springer Nature}, author={Mertens, Jan Cedric and Boschmann, Alexander and Schmidt, M. and Plessl, Christian}, year={2018}, pages={441–451} }","mla":"Mertens, Jan Cedric, et al. “Sprint Diagnostic with GPS and Inertial Sensor Fusion.” Sports Engineering, vol. 21, no. 4, Springer Nature, 2018, pp. 441–51, doi:10.1007/s12283-018-0291-0."},"year":"2018","page":"441-451"},{"oa":"1","date_updated":"2022-01-12T16:32:23Z","language":[{"iso":"eng"}],"title":"Accelerating Molecular Dynamic Simulations by Offloading Fast Fourier Transformations to FPGA","project":[{"name":"SFB 901","_id":"1"},{"_id":"4","name":"SFB 901 - Project Area C"},{"_id":"14","name":"SFB 901 - Subproject C2"}],"department":[{"_id":"27"},{"_id":"518"}],"_id":"5417","year":"2018","citation":{"short":"A. Ramaswami, Accelerating Molecular Dynamic Simulations by Offloading Fast Fourier Transformations to FPGA, Universität Paderborn, 2018.","ieee":"A. Ramaswami, Accelerating Molecular Dynamic Simulations by Offloading Fast Fourier Transformations to FPGA. Universität Paderborn, 2018.","apa":"Ramaswami, A. (2018). Accelerating Molecular Dynamic Simulations by Offloading Fast Fourier Transformations to FPGA. Universität Paderborn.","ama":"Ramaswami A. Accelerating Molecular Dynamic Simulations by Offloading Fast Fourier Transformations to FPGA. Universität Paderborn; 2018.","chicago":"Ramaswami, Arjun. Accelerating Molecular Dynamic Simulations by Offloading Fast Fourier Transformations to FPGA. Universität Paderborn, 2018.","bibtex":"@book{Ramaswami_2018, title={Accelerating Molecular Dynamic Simulations by Offloading Fast Fourier Transformations to FPGA}, publisher={Universität Paderborn}, author={Ramaswami, Arjun}, year={2018} }","mla":"Ramaswami, Arjun. Accelerating Molecular Dynamic Simulations by Offloading Fast Fourier Transformations to FPGA. Universität Paderborn, 2018."},"type":"mastersthesis","supervisor":[{"id":"16153","last_name":"Plessl","orcid":"0000-0001-5728-9982","full_name":"Plessl, Christian","first_name":"Christian"}],"main_file_link":[{"open_access":"1"}],"ddc":["000"],"user_id":"49171","abstract":[{"text":"Molecular Dynamic (MD) simulations are computationally intensive and accelerating them using specialized hardware is a topic of investigation in many studies. One of the routines in the critical path of MD simulations is the three-dimensional Fast Fourier Transformation (FFT3d). The potential in accelerating FFT3d using hardware is usually bound by bandwidth and memory. Therefore, designing a high throughput solution for an FPGA that overcomes this problem is challenging.\r\nIn this thesis, the feasibility of offloading FFT3d computations to FPGA implemented using OpenCL is investigated. In order to mask the latency in memory access, an FFT3d that overlaps computation with communication is designed. The implementa- tion of this design is synthesized for the Arria 10 GX 1150 FPGA and evaluated with the FFTW benchmark. Analysis shows a better performance using FPGA over CPU for larger FFT sizes, with the 643 FFT showing a 70% improvement in runtime using FPGAs.\r\nThis FFT3d design is integrated with CP2K to explore the potential in accelerating molecular dynamic simulations. Evaluation of CP2K simulations using FPGA shows a 41% improvement in runtime in FFT3d computations over CPU for larger FFT3d designs.","lang":"eng"}],"has_accepted_license":"1","status":"public","date_created":"2018-11-07T16:08:32Z","publisher":"Universität Paderborn","author":[{"last_name":"Ramaswami","id":"49171","first_name":"Arjun","orcid":"https://orcid.org/0000-0002-0909-1178","full_name":"Ramaswami, Arjun"}],"file_date_updated":"2020-06-15T11:29:38Z","keyword":["FFT: FPGA","CP2K","OpenCL"],"file":[{"file_name":"masterthesis.pdf","date_created":"2020-06-15T11:29:38Z","access_level":"closed","creator":"arjunr","file_id":"17093","file_size":1297585,"relation":"main_file","success":1,"content_type":"application/pdf","date_updated":"2020-06-15T11:29:38Z"}]},{"date_updated":"2023-09-26T11:47:52Z","doi":"10.1109/FCCM.2018.00037","language":[{"iso":"eng"}],"title":"OpenCL-based FPGA Design to Accelerate the Nodal Discontinuous Galerkin Method for Unstructured Meshes","department":[{"_id":"27"},{"_id":"518"},{"_id":"61"}],"project":[{"_id":"33","name":"HighPerMeshes","grant_number":"01|H16005A"},{"_id":"1","grant_number":"160364472","name":"SFB 901"},{"_id":"4","name":"SFB 901 - Project Area C"},{"grant_number":"160364472","name":"SFB 901 - Subproject C2","_id":"14"}],"conference":{"name":"Proc. Int. Symp. on Field-Programmable Custom Computing Machines (FCCM)"},"_id":"1588","year":"2018","citation":{"ieee":"T. Kenter et al., “OpenCL-based FPGA Design to Accelerate the Nodal Discontinuous Galerkin Method for Unstructured Meshes,” presented at the Proc. Int. Symp. on Field-Programmable Custom Computing Machines (FCCM), 2018, doi: 10.1109/FCCM.2018.00037.","short":"T. Kenter, G. Mahale, S. Alhaddad, Y. Grynko, C. Schmitt, A. Afzal, F. Hannig, J. Förstner, C. Plessl, in: Proc. Int. Symp. on Field-Programmable Custom Computing Machines (FCCM), IEEE, 2018.","mla":"Kenter, Tobias, et al. “OpenCL-Based FPGA Design to Accelerate the Nodal Discontinuous Galerkin Method for Unstructured Meshes.” Proc. Int. Symp. on Field-Programmable Custom Computing Machines (FCCM), IEEE, 2018, doi:10.1109/FCCM.2018.00037.","bibtex":"@inproceedings{Kenter_Mahale_Alhaddad_Grynko_Schmitt_Afzal_Hannig_Förstner_Plessl_2018, title={OpenCL-based FPGA Design to Accelerate the Nodal Discontinuous Galerkin Method for Unstructured Meshes}, DOI={10.1109/FCCM.2018.00037}, booktitle={Proc. Int. Symp. on Field-Programmable Custom Computing Machines (FCCM)}, publisher={IEEE}, author={Kenter, Tobias and Mahale, Gopinath and Alhaddad, Samer and Grynko, Yevgen and Schmitt, Christian and Afzal, Ayesha and Hannig, Frank and Förstner, Jens and Plessl, Christian}, year={2018} }","apa":"Kenter, T., Mahale, G., Alhaddad, S., Grynko, Y., Schmitt, C., Afzal, A., Hannig, F., Förstner, J., & Plessl, C. (2018). OpenCL-based FPGA Design to Accelerate the Nodal Discontinuous Galerkin Method for Unstructured Meshes. Proc. Int. Symp. on Field-Programmable Custom Computing Machines (FCCM). Proc. Int. Symp. on Field-Programmable Custom Computing Machines (FCCM). https://doi.org/10.1109/FCCM.2018.00037","ama":"Kenter T, Mahale G, Alhaddad S, et al. OpenCL-based FPGA Design to Accelerate the Nodal Discontinuous Galerkin Method for Unstructured Meshes. In: Proc. Int. Symp. on Field-Programmable Custom Computing Machines (FCCM). IEEE; 2018. doi:10.1109/FCCM.2018.00037","chicago":"Kenter, Tobias, Gopinath Mahale, Samer Alhaddad, Yevgen Grynko, Christian Schmitt, Ayesha Afzal, Frank Hannig, Jens Förstner, and Christian Plessl. “OpenCL-Based FPGA Design to Accelerate the Nodal Discontinuous Galerkin Method for Unstructured Meshes.” In Proc. Int. Symp. on Field-Programmable Custom Computing Machines (FCCM). IEEE, 2018. https://doi.org/10.1109/FCCM.2018.00037."},"type":"conference","abstract":[{"lang":"eng","text":"The exploration of FPGAs as accelerators for scientific simulations has so far mostly been focused on small kernels of methods working on regular data structures, for example in the form of stencil computations for finite difference methods. In computational sciences, often more advanced methods are employed that promise better stability, convergence, locality and scaling. Unstructured meshes are shown to be more effective and more accurate, compared to regular grids, in representing computation domains of various shapes. Using unstructured meshes, the discontinuous Galerkin method preserves the ability to perform explicit local update operations for simulations in the time domain. In this work, we investigate FPGAs as target platform for an implementation of the nodal discontinuous Galerkin method to find time-domain solutions of Maxwell's equations in an unstructured mesh. When maximizing data reuse and fitting constant coefficients into suitably partitioned on-chip memory, high computational intensity allows us to implement and feed wide data paths with hundreds of floating point operators. By decoupling off-chip memory accesses from the computations, high memory bandwidth can be sustained, even for the irregular access pattern required by parts of the application. Using the Intel/Altera OpenCL SDK for FPGAs, we present different implementation variants for different polynomial orders of the method. In different phases of the algorithm, either computational or bandwidth limits of the Arria 10 platform are almost reached, thus outperforming a highly multithreaded CPU implementation by around 2x."}],"ddc":["000"],"user_id":"15278","publication":"Proc. Int. Symp. on Field-Programmable Custom Computing Machines (FCCM)","file_date_updated":"2018-11-02T14:45:05Z","keyword":["tet_topic_hpc"],"quality_controlled":"1","publisher":"IEEE","author":[{"full_name":"Kenter, Tobias","first_name":"Tobias","id":"3145","last_name":"Kenter"},{"last_name":"Mahale","first_name":"Gopinath","full_name":"Mahale, Gopinath"},{"full_name":"Alhaddad, Samer","first_name":"Samer","id":"42456","last_name":"Alhaddad"},{"full_name":"Grynko, Yevgen","first_name":"Yevgen","id":"26059","last_name":"Grynko"},{"last_name":"Schmitt","full_name":"Schmitt, Christian","first_name":"Christian"},{"last_name":"Afzal","first_name":"Ayesha","full_name":"Afzal, Ayesha"},{"full_name":"Hannig, Frank","first_name":"Frank","last_name":"Hannig"},{"id":"158","last_name":"Förstner","orcid":"0000-0001-7059-9862","full_name":"Förstner, Jens","first_name":"Jens"},{"first_name":"Christian","full_name":"Plessl, Christian","orcid":"0000-0001-5728-9982","last_name":"Plessl","id":"16153"}],"file":[{"date_created":"2018-11-02T14:45:05Z","file_name":"08457652.pdf","access_level":"closed","file_size":269130,"file_id":"5282","creator":"ups","date_updated":"2018-11-02T14:45:05Z","content_type":"application/pdf","success":1,"relation":"main_file"}],"date_created":"2018-03-22T10:48:01Z","has_accepted_license":"1","status":"public"},{"publication_identifier":{"isbn":["978-1-4503-5891-0/18/07"]},"project":[{"_id":"32","name":"Performance and Efficiency in HPC with Custom Computing","grant_number":"PL 595/2-1 / 320898746"},{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"department":[{"_id":"27"},{"_id":"518"},{"_id":"304"}],"title":"A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices","external_id":{"arxiv":["1710.10899"]},"place":"New York, NY, USA","language":[{"iso":"eng"}],"doi":"10.1145/3218176.3218231","date_updated":"2023-09-26T11:48:12Z","date_created":"2018-03-22T10:53:01Z","status":"public","keyword":["approximate computing","linear algebra","matrix inversion","matrix p-th roots","numeric algorithm","parallel computing"],"publication":"Proc. Platform for Advanced Scientific Computing (PASC) Conference","author":[{"first_name":"Michael","full_name":"Lass, Michael","orcid":"0000-0002-5708-7632","last_name":"Lass","id":"24135"},{"last_name":"Mohr","full_name":"Mohr, Stephan","first_name":"Stephan"},{"first_name":"Hendrik","full_name":"Wiebeler, Hendrik","last_name":"Wiebeler"},{"id":"49079","last_name":"Kühne","full_name":"Kühne, Thomas","first_name":"Thomas"},{"full_name":"Plessl, Christian","orcid":"0000-0001-5728-9982","first_name":"Christian","id":"16153","last_name":"Plessl"}],"publisher":"ACM","quality_controlled":"1","user_id":"15278","abstract":[{"text":"We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. Following the idea of Approximate Computing, we allow imprecision in the final result in order to utilize the sparsity of the input matrix and to allow massively parallel execution. For an n x n matrix, the proposed algorithm allows to distribute the calculations over n nodes with only little communication overhead. The result matrix exhibits the same sparsity pattern as the input matrix, allowing for efficient reuse of allocated data structures.\r\n\r\nWe evaluate the algorithm with respect to the error that it introduces into calculated results, as well as its performance and scalability. We demonstrate that the error is relatively limited for well-conditioned matrices and that results are still valuable for error-resilient applications like preconditioning even for ill-conditioned matrices. We discuss the execution time and scaling of the algorithm on a theoretical level and present a distributed implementation of the algorithm using MPI and OpenMP. We demonstrate the scalability of this implementation by running it on a high-performance compute cluster comprised of 1024 CPU cores, showing a speedup of 665x compared to single-threaded execution.","lang":"eng"}],"year":"2018","citation":{"ieee":"M. Lass, S. Mohr, H. Wiebeler, T. Kühne, and C. Plessl, “A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices,” presented at the Platform for Advanced Scientific Computing Conference (PASC), Basel, Switzerland, 2018, doi: 10.1145/3218176.3218231.","short":"M. Lass, S. Mohr, H. Wiebeler, T. Kühne, C. Plessl, in: Proc. Platform for Advanced Scientific Computing (PASC) Conference, ACM, New York, NY, USA, 2018.","mla":"Lass, Michael, et al. “A Massively Parallel Algorithm for the Approximate Calculation of Inverse P-Th Roots of Large Sparse Matrices.” Proc. Platform for Advanced Scientific Computing (PASC) Conference, ACM, 2018, doi:10.1145/3218176.3218231.","bibtex":"@inproceedings{Lass_Mohr_Wiebeler_Kühne_Plessl_2018, place={New York, NY, USA}, title={A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices}, DOI={10.1145/3218176.3218231}, booktitle={Proc. Platform for Advanced Scientific Computing (PASC) Conference}, publisher={ACM}, author={Lass, Michael and Mohr, Stephan and Wiebeler, Hendrik and Kühne, Thomas and Plessl, Christian}, year={2018} }","chicago":"Lass, Michael, Stephan Mohr, Hendrik Wiebeler, Thomas Kühne, and Christian Plessl. “A Massively Parallel Algorithm for the Approximate Calculation of Inverse P-Th Roots of Large Sparse Matrices.” In Proc. Platform for Advanced Scientific Computing (PASC) Conference. New York, NY, USA: ACM, 2018. https://doi.org/10.1145/3218176.3218231.","ama":"Lass M, Mohr S, Wiebeler H, Kühne T, Plessl C. A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices. In: Proc. Platform for Advanced Scientific Computing (PASC) Conference. ACM; 2018. doi:10.1145/3218176.3218231","apa":"Lass, M., Mohr, S., Wiebeler, H., Kühne, T., & Plessl, C. (2018). A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices. Proc. Platform for Advanced Scientific Computing (PASC) Conference. Platform for Advanced Scientific Computing Conference (PASC), Basel, Switzerland. https://doi.org/10.1145/3218176.3218231"},"type":"conference","conference":{"end_date":"2018-07-04","location":"Basel, Switzerland","start_date":"2018-07-02","name":"Platform for Advanced Scientific Computing Conference (PASC)"},"_id":"1590"},{"doi":"10.1145/3178487.3178534","date_updated":"2023-09-26T11:47:23Z","language":[{"iso":"eng"}],"title":"Automated Code Acceleration Targeting Heterogeneous OpenCL Devices","project":[{"_id":"1","name":"SFB 901","grant_number":"160364472"},{"_id":"4","name":"SFB 901 - Project Area C"},{"_id":"14","name":"SFB 901 - Subproject C2","grant_number":"160364472"}],"publication_status":"published","publication_identifier":{"isbn":["9781450349826"]},"department":[{"_id":"27"},{"_id":"518"}],"_id":"1204","citation":{"bibtex":"@inproceedings{Riebler_Vaz_Kenter_Plessl_2018, title={Automated Code Acceleration Targeting Heterogeneous OpenCL Devices}, DOI={10.1145/3178487.3178534}, booktitle={Proc. ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP)}, publisher={ACM}, author={Riebler, Heinrich and Vaz, Gavin Francis and Kenter, Tobias and Plessl, Christian}, year={2018} }","mla":"Riebler, Heinrich, et al. “Automated Code Acceleration Targeting Heterogeneous OpenCL Devices.” Proc. ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP), ACM, 2018, doi:10.1145/3178487.3178534.","apa":"Riebler, H., Vaz, G. F., Kenter, T., & Plessl, C. (2018). Automated Code Acceleration Targeting Heterogeneous OpenCL Devices. Proc. ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP). https://doi.org/10.1145/3178487.3178534","ama":"Riebler H, Vaz GF, Kenter T, Plessl C. Automated Code Acceleration Targeting Heterogeneous OpenCL Devices. In: Proc. ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP). ACM; 2018. doi:10.1145/3178487.3178534","chicago":"Riebler, Heinrich, Gavin Francis Vaz, Tobias Kenter, and Christian Plessl. “Automated Code Acceleration Targeting Heterogeneous OpenCL Devices.” In Proc. ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP). ACM, 2018. https://doi.org/10.1145/3178487.3178534.","ieee":"H. Riebler, G. F. Vaz, T. Kenter, and C. Plessl, “Automated Code Acceleration Targeting Heterogeneous OpenCL Devices,” 2018, doi: 10.1145/3178487.3178534.","short":"H. Riebler, G.F. Vaz, T. Kenter, C. Plessl, in: Proc. ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP), ACM, 2018."},"year":"2018","type":"conference","user_id":"15278","ddc":["000"],"has_accepted_license":"1","status":"public","date_created":"2018-03-08T14:45:18Z","file":[{"file_size":447769,"creator":"ups","file_id":"5281","date_updated":"2018-11-02T14:43:37Z","content_type":"application/pdf","success":1,"relation":"main_file","date_created":"2018-11-02T14:43:37Z","file_name":"p417-riebler.pdf","access_level":"closed"}],"author":[{"last_name":"Riebler","id":"8961","first_name":"Heinrich","full_name":"Riebler, Heinrich"},{"full_name":"Vaz, Gavin Francis","first_name":"Gavin Francis","id":"30332","last_name":"Vaz"},{"first_name":"Tobias","full_name":"Kenter, Tobias","last_name":"Kenter","id":"3145"},{"full_name":"Plessl, Christian","orcid":"0000-0001-5728-9982","first_name":"Christian","id":"16153","last_name":"Plessl"}],"publisher":"ACM","quality_controlled":"1","keyword":["htrop"],"file_date_updated":"2018-11-02T14:43:37Z","publication":"Proc. ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP)"}]