Description: High-order vector finite element method in EM
|(undirected graph drawing)|
|number of rows||1,157,456|
|number of columns||1,157,456|
|structural full rank?||yes|
|# of blocks from dmperm||1|
|# strongly connected comp.||1|
|explicit zero entries||0|
|nonzero pattern symmetry||symmetric|
|numeric value symmetry||symmetric|
|author||A. Dziekonski, A. Lamecki, M. Mrozowski|
|Additional fields||size and type|
High order vector finite element method in electromagnetics The dielFilter* matrices came from analysis of a 4th-pole dielectric resonator  generated with Finite Element Method. The tetrahedral mesh of the structure was generated with the Netgen mesher . The matrices were used as an example in our paper . dielFilterV2clx - complex symmetric matrix (607,232 x 607,232), 25,309,272 nonzero (real) and 728,900 nonzero (imag) elements. First 109,108 unknowns correspond to lowest level base functions. dielFilterV2real - real symmetric matrix (1,157,456 x 1,157,456) and 48,538,952 nonzero elements. First 209,432 unknowns correspond to lowest level base functions. dielFilterV3clx - complex symmetric matrix (420,408 x 420,408), 32,886,208 nonzero (real) and 3,706,513 (imag) elements. First 24,716 unknowns correspond to lowest level base functions, next 116,152 unknowns correspond to the second level. dielFilterV3real - real symmetric matrix (1,102,824 x 1,102,824) and 89,306,020 nonzero elements. First 66,353 unknowns correspond to lowest level base functions, next 305,729 unknowns correspond to the second level. All matrices are sparse and come with right-hand-sides.  J. Schoberl, "NETGEN An advancing front 2D/3D-mesh generator based on abstract rules," Computing and Visualization in Science, vol. 1, No. 1, pp. 41-52, July 1997  A. Dziekonski, A. Lamecki, M. Mrozowski, Tuning A Hybrid GPU-CPU V-cycle Multilevel Preconditioner for Solving Large Real and Complex Systems of FEM Equations.  F. Alessandri, M. Chiodetti, A. Giugliarelli; D. Maiarelli, G. Martirano, D. Schmitt, L. Vanni and F. Vitulli. The electric-field Integral-equation method for the analysis and design of a class of rectangular cavity filters loaded by dielectric and metallic cylindrical pucks, Microwave Theory and Techniques, IEEE Transactions on, vol. 52, no 8, pp. 1790-1797, Aug. 2004.
|nnz(chol(P*(A+A'+s*I)*P')) with AMD||1,160,556,168|
|Cholesky flop count||4.8e+12|
|nnz(L+U), no partial pivoting, with AMD||2,319,954,880|
|nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD||2,693,105,368|
|nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD||6,428,054,924|
For a description of the statistics displayed above, click here.
Maintained by Tim Davis, last updated 12-Mar-2014.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.