Abstract
We present ideas and first results on a GPU acceleration of a non-linear solver embedded into the biomedical application code CARP. The linear system solvers have been transferred already in the past and so we concentrate on how to extend the GPU acceleration to larger portions of the code. The finite element assembling of stiffness and mass matrices takes at least 50 % of the CPU time and therefore we investigate this process for the bidomain equations but with focus on later use in non-linear and/or time-dependent problems. The CUDA code for matrix calculation and assembling is faster by a factor up to \(90\) compared to a single CPU core. The routines were integrated to CARP’s main code and they are already used to assemble the FE matrices of the bidomain model. Further performance studies are still required for the bidomain-mechanics model.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bell, N., Dalton, S., Olson, L.N.: Exposing fine-grained parallelism in algebraic multigrid methods. SIAM J. Sci. Comput. 34(2), C123–C152 (2012)
Cecka, C., Lew, A.J., Darve, E.: Assembly of finite element methods on graphics processors. Int. J. Numer. Methods Eng. 85(5), 640–669 (2011)
Geveler, M., Ribbrock, D., Göddeke, D., Zajac, P., Turek, S.: Towards a complete FEM-based simulation toolkit on GPUs: unstructured grid finite element geometric multigrid solvers with strong smoothers based on sparse approximate inverses. Comput. Fluids 80, 327–332 (2013)
Gockenbach, M.S.: Understanding and Implementing the Finite Element Method. SIAM, Philadelphia (2007)
Göddeke, D.: Fast and accurate finite-element multigrid solvers for PDE simulations on GPU clusters. Ph.D. thesis, Technische Universität Dortmund, Fakultät für Mathematik, May 2010. http://hdl.handle.net/2003/27243
Göddeke, D., Strzodka, R., Mohd-Yusof, J., McCormick, P.S., Wobker, H., Becker, C., Turek, S.: Using GPUs to improve multigrid solver performance on a cluster. Int. J. Comput. Sci. Eng. 4(1), 36–55 (2008)
Haase, G., Liebmann, M., Douglas, C.C., Plank, G.: A parallel algebraic multigrid solver on graphics processing units. In: Zhang, W., Chen, Z., Douglas, C.C., Tong, W. (eds.) HPCA 2009. LNCS, vol. 5938, pp. 38–47. Springer, Heidelberg (2010)
Jónasson, K. (ed.): PARA 2010, Part II. LNCS, vol. 7134. Springer, Heidelberg (2012)
Jung, M., Langer, U.: Methode der finiten Elemente für Ingenieure. Lehrbuch, 2nd edn. Springer Vieweg, Wiesbaden (2013)
Larson, M.G., Bengzon, F.: The Finite Element Method: Theory, Implementations and Applications. Texts in Computational Science and Engineering, vol. 10, 1st edn. Springer, Heidelberg (2013)
Markall, G.R., Slemmer, A., Ham, D.A., Kelly, P.H.J., Cantwell, C.D., Sherwin, S.J.: Finite element assembly strategies on multi-core and many-core architectures. Int. J. Numer. Methods Fluids 71(1), 80–97 (2013)
Neic, A., Liebmann, M., Haase, G., Plank, G.: Algebraic multigrid solvers on clusters of CPUs and GPUs. In: Jónasson [8], pp. 389–398
Neic, A., Liebmann, M., Hötzl, E., Mitchell, L., Vigmond, E., Haase, G., Plank, G.: Accelerating cardiac bidomain simulations using graphics processing units. IEEE Trans. Biomed. Eng. 59(8), 2281–2290 (2012)
NVIDIA Corporation. CUDA programming guide 5.0 (2012). http://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html
Pathmanathan, P., Whiteley, J.P.: A numerical method for cardiac mechanoelectric simulations. Ann. Biomed. Eng. 37(5), 860–873 (2009)
Rocha, B., Campos, F., Plank, G., Weber dos Santos, R., Liebmann, M., Haase, G.: Simulations of the electrical activity in the heart with graphic processing units. Concur. Comput. Pract. Exp. 23, 708–720 (2011)
Tracy, F.T.: Optimizing finite element programs on the cray X1 using coloring schemes. In: Proceedings of the 2004 Users Group Conference, \(\text{ DOD }\!\!\_\!\!\text{ UGC } \text{'04 }\), pp. 329–333. IEEE Computer Society, Washington, DC, USA (2004)
Vigmond, E., Hughes, M., Plank, G., Leon, L.: Computational tools for modeling electrical activity in cardiac tissue. J. Electrocardiol. 36, 69–74 (2003)
Vigmond, E., Plank, G.: Cardiac arrhythmia research package (2009). http://carp.meduni-graz.at
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Costa, C.M., Haase, G., Liebmann, M., Neic, A., Plank, G. (2014). Stepping into Fully GPU Accelerated Biomedical Applications. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2013. Lecture Notes in Computer Science(), vol 8353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43880-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-662-43880-0_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-43879-4
Online ISBN: 978-3-662-43880-0
eBook Packages: Computer ScienceComputer Science (R0)