Guettel/TEM181302

3D transient electromagnetic modelling, S. Guettel, Univ Manchester
Name TEM181302
Group Guettel
Matrix ID 2813
Num Rows 181,302
Num Cols 181,302
Nonzeros 7,839,010
Pattern Entries 7,839,010
Kind Electromagnetics Problem
Symmetric Yes
Date 2015
Author R.-U. B\"orner, O. G. Ernst, S. G\"uttel
Editor T. Davis
Structural Rank 181,302
Structural Rank Full true
Num Dmperm Blocks 1
Strongly Connect Components 1
Num Explicit Zeros 0
Pattern Symmetry 100%
Numeric Symmetry 100%
Cholesky Candidate yes
Positive Definite no
Type real
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Notes
3D Transient Electromagnetic Modelleing, Stefan Guettel, Univ Manchester
                                                                        
The TEM problem relates to the time-dependent modelling of a transient  
electromagnetic field in geophysical exploration. The set contains a    
matrix pencil (C,M) and an initial value vector q, corresponding to a   
Nedelec finite element discretization of Maxwell's equations for the    
electric field density e(t). The curl-curl matrix C is symmetric        
positive semi-definite and the mass matrix M is symmetric positive      
definite. The problem to be solved is a linear initial value problem    
                                                                        
   M*e'(t) = C*e(t),  M*e(0) = q,                                       
                                                                        
for logarithmically distributed time points t in the interval           
[1e-6,1e-3].                                                            
                                                                        
There are three test sets which are described in the following          
publication:                                                            
                                                                        
@article{BEG2015,                                                       
  title={Three-dimensional transient electromagnetic modelling using    
    rational {K}rylov methods},                                         
  author={B{\"o}rner, Ralph-Uwe and Ernst, Oliver G and G{\"u}ttel,     
    Stefan},                                                            
  journal={Geophysical Journal International},                          
  volume={202},                                                         
  number={3},                                                           
  pages={2025--2043},                                                   
  year={2015},                                                          
  publisher={Oxford University Press}                                   
}                                                                       
                                                                        
The problem details are                                                 
                                                                        
TEM27623: section 5.1 in the above paper; layered half-space problem    
discretized by 24582 tetrahedral elements of order 1 giving rise to     
27623 degrees of freedom.                                               
                                                                        
TEM152078: section 5.1 in the above paper; layered half-space problem   
discretized by 24582 tetrahedral elements of order 2 giving rise to     
152078 degrees of freedom.                                              
                                                                        
TEM181302: section 5.2 in the above paper; homogeneous subsurface with  
topography discretized by 28849 tetrahedral elements of order 2 giving  
rise to 181302 degrees of freedom.                                      
                                                                        
In the SuiteSparse Matrix Collection, the primary matrix Problem.A is   
the matrix C in the TEM* problems.  The M matrix appears as             
Problem.aux.M, and the q vector is Problem.aux.q.