This Polynomial Eigenvalue Problem Collection (PEPCo) includes degree n polynomial eigenvalue problems in the form

Description of File Name

The file names consists the following information：

• Name of the problem
• Degree of the PEP[S/G: standard/generalized EP; 2,3,4,...: degree of PEP]
• Matrix size[UserDef: user defined]
• Matrix element data type[S/D: single/double real number; C/Z: single/double complex number]
• File format[MMX, MATLAB p-code/m-code, Linux Executable, Fortran, C]
• Reference describing the problem in detail

File Name Example

The file "Q1-5-186543-D-MMX-10a.tar.gz" contains the problem "Q1", which is a "degree 2" PEP with matrix size "186,543" in "double real numbers". The coefficient matrices are stored in the "MMX" format. The details of this test problem can be found in "[10a]".

Standard Eigenvalue Problems

3D pyramid quantum dot simulation (with constant effective mass model and uniform finite volume mesh)

• PyrQD-1-UserDef-D-LnxExe-04a.zip
• This problem generator can construct test problems in Tables 1 and 5 of [04a]. The matrix dimensions of the problems are 2475, 22103, 186543, 1532255, 12419775, and 32401863.

Generalized Eigenvalue Problems

3D Irregular Shape Quantum Dot Simulation (with constant effective mass model)

• IrregQD-G-UserDef-D-LnxExe-07a.zip
• This problem generator can generate the 5 problems listed in Table 1 of [07a].
• The dimension of these problems are 1180, 10919, 99176, 895307, and 8065940.

Degree 3 Polynomial Eigenvalue Problems

3D cylindrical quantum dot simulation (with non-parabolic effective mass model and non-uniform finite difference mesh)

• CylQD-3-UserDef-D-MATLABp-03a.zip
• This problem generator can generate the 9 problems compared in Figure 3 of [03a].
• The dimension of Case 1 problems are 43078, 172558, and 690718.
• The dimension of Case 2 problems are 49950, 186150, and 717750.
• The dimension of Case 3 problems are 58900, 203500, and 751900.

• CylQD-3-UserDef-D-LnxExe-03a.zip
• This problem generator can construct test problems in Cases 1, 2, and 3 of [03a] (9 problems in Figure 3), Subcase 3.1 (1 problem in Table 4), Subcase 3.2 (9 problems in Table 5).
• C1-3-101650-D-MMX-10a.tar.tz (The test problem C1 described in Table 2 of [10a].)
• C2-3-1006200-D-MMX-10a.tar.tz (The test problem C2 described in Table 2 of [10a].)
• C3-3-1008618-D-MMX-10a.tar.tz (The test problem C3 described in Table 2 of [10a].)

Degree 5 Polynomial Eigenvalue Problems

3D Pyramidal Quantum Dot Simulation (with non-parabolic effective mass model)

• PyrQD-5-UserDef-D-LnxExe-04a.zip
• This problem generator can generate the 6 test problems described in Tables 1 and 5 of [04a].
• The dimension of these test problems are 2475, 22103, 186543, 1532255, 12419775, and 32401863.
• Note that the problems with dimension 186543, 1532255, and 32401863 are also Problems Q1, Q2, and Q3 listed in Table 2 of [10a], respectively.
• Q1-5-186543-D-MMX-10a.tar.gz (The test problem Q1 described in Table 2 of [10a].)
• Q2-5-1532255-D-MMX-10a.zip (The test problem Q2 described in Table 2 of [10a].)
• Q3-5-32401863-D-MMX-10a.zip (The test problem Q3 described in Table 2 of [10a].)

References

• [03a] Weichung Wang*, Tsung-Min Hwang, Wen-Wei Lin, and Jinn-Liang Liu (2003). "Numerical Methods for Semiconductor Heterostructures with Band Nonparabolicity," Journal of Computational Physics, 190(1): 141-158. http://dx.doi.org/10.1016/S0021-9991(03)00268-7
• [04a] Tsung-Min Hwang, Wen-Wei Lin, Wei-Cheng Wang, and Weichung Wang*, (2004). "Numerical Simulation of Three Dimensional Pyramid Quantum Dot," Journal of Computational Physics, 196(1): 208-232. http://dx.doi.org/10.1016/j.jcp.2003.10.026
• [07a] Tsung-Min Hwang, Wei-Cheng Wang, and Weichung Wang (2007). "Numerical Schemes for Three Dimensional Irregular Shape Quantum Dots over Curvilinear Coordinate Systems," Journal of Computational Physics, 226(1):754-773. http://dx.doi.org/10.1016/j.jcp.2007.04.022
• [08a] Tsung-Min Hwang, Wei-Hua Wang, and Weichung Wang* (2008). "Efficient Numerical Schemes for Electronic States in Coupled Quantum Dots," Journal of Nanoscience and Nanotechnology, 8(7):3695–3709. http://dx.doi.org/10.1166/jnn.2008.004
• [10a] Feng-Nan Hwang, Zih-Hao Wei, Tsung-Ming Huang, and Weichung Wang (2010). “A Parallel Additive Schwarz Preconditioned Jacobi-Davidson Algorithm for Polynomial Eigenvalue Problems in Quantum Dot Simulation." Journal of Computational Physics, 229(8):2932-2947. http://dx.doi.org/10.1016/j.jcp.2009.12.024

We provide a generator of the coefficient matrices of the generalized eigenvalue problems that arise from modeling leaky surface wave propagation in an acoustic resonator with an infinite amount of periodically arranged interdigital transducers. The constitutive equations are discretized by finite element methods with mesh refinements along the electrode interfaces and corners.

Syntax:

[mtx_M1, mtx_M2, mtx_F, mtx_G] = mtx_SAW_filter(test_case, omega, mesh_size, refine_level)

Input variables:

• test_case : benchmark problem ('LiNbO_3', or, 'LiTaO_3', or 'quartz')
• omega : frequency
• mesh_size : length of the mesh
• refine_level : level of the refining (0: uniform mesh, 2: non-uniform mesh)

• Download (mtx_SAW_filter.zip)
• License: Copyright (c) 2018 by Tsung-Ming Huang, Wen-Wei Lin and Chin-Tien Wu
• Reference:

1. Tsung-Ming Huang, Wen-Wei Lin and Chin-Tien Wu, Structure-preserving Arnoldi-type algorithm for solving eigenvalue problems in Leaky surface wave propagation, Applied Mathematics and Computation, Vol. 219, 9947-9958, 2013.
2. Tsung-Ming Huang, Tiexiang Li, Wen-Wei Lin and Chin-Tien Wu, Numerical studies on structure-preserving algorithms for surface acoustic wave simulations, Journal of Computational and Applied Mathematics, Vol. 244, pp. 140-154, 2013.