Abstract
We describe a multilevel adaptive grid refinement package designed to provide a high performance, serial or parallel patch class for use in PDE solvers. We provide a high level description algorithmically with mathematical motivation. The C++ code uses cache aware data structures and automatically load balances.
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Agmon, S.: Lectures on Elliptic Boundary Value Problems. Van Nostrand Reinhold, New York, 1965.
Berger, M.J., AND Colella, P.: Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82 (1989), 64–84.
Berger, M.J., AND Oliger, J.: An adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys. 53 (1984), 484–512.
Boor, C.: A Practical Guide to Splines. Springer-Verlag, New York, 1978.
Briggs, W.L., Henson, V.E., AND Mcormick, S.F.: A Multigrid Tutorial. SIAM Books, Philadelphia, 2000. Second edition.
Devine, K., Hendrickson, B., Boman, E., ST. John, M., AND Vaughan, C.: Design of dynamic load-balancing tools for parallel applications. In Proc. International Conference on Supercomputing (Santa Fe, 2000).
Douglas, C.C.: Caching in with multigrid algorithms: problems in two dimensions. Paral. Alg. Appl. 9 (1996), 195–204.
Douglas, C.C., Haase, G., AND Langer, U.: A tutorial on elliptic pde’s and parallel solution methods. http://www.mgnet.org/~douglas/ccd-preprints.html, 2002.
Douglas, C.C., Hu, J., Kowarschik, M., Rüde, U., AND Weiss, C.: Cache optimization for structured and unstructured grid multigrid. Elect. Trans. Numer. Anal. 10 (2000), 21–40.
Hu, J.: Cache Based Multigrid on Unstructured Grids in Two and Three Dimensions. PhD thesis, University of Kentucky, Department of Mathematics, Lexington, KY, 2000.
Martin, D., AND Cartwright, K.: Solving Poisson’s equation using adaptive mesh refinement. http://seesar.lbl.gov/anag/staff/martin/tar/AMR.ps, 1996.
Mcormick, S.F.: The fast adaptive composite (FAC) method for elliptic equations. Math. Comp. 46 (1986), 439–456.
Morton, K.W., AND Mayers, D.F.: Numerical Solution of Partial Differential Equations. Cambridge University Press, Cambridge, 1994.
Parashar, M.: GrACE. http://www.caip.rutgers.edu/~parashar/TASSL/Projects/ GrACE, 2001.
Rüde, U.: Mathematical and Computational Techniques for Multilevel Adaptive Methods, vol. 13 of Frontiers in Applied Mathematics. SIAM, Philadelphia, 1993.
Varga, R.S.: Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1962.
Weiss et al, C.: Dimepack. http://wwwbode.cs.tum.edu/Par/arch/cache.
Yserentant, H.: On the multi-level splitting of finite element spaces. Numer. Math. 49 (1986), 379–412.
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Douglas, C.C., Hu, J., Ray, J., Thorne, D., Tuminaro, R. (2002). Fast, Adaptively Refined Computational Elements in 3D. In: Sloot, P.M.A., Hoekstra, A.G., Tan, C.J.K., Dongarra, J.J. (eds) Computational Science — ICCS 2002. ICCS 2002. Lecture Notes in Computer Science, vol 2331. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47789-6_80
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DOI: https://doi.org/10.1007/3-540-47789-6_80
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