7 Numerical modeling part II: linearizations, nonlinear solvers, and linear solution

2020 ◽  
pp. 131-168
2012 ◽  
Vol 20 (3) ◽  
pp. 311-325 ◽  
Author(s):  
William F. Spotz

PyTrilinos is a set of Python interfaces to compiled Trilinos packages. This collection supports serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, algebraic and multilevel preconditioners, nonlinear solvers and continuation algorithms, eigensolvers and partitioning algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are compatible with the popular NumPy Python package. As a Python front end to compiled libraries, PyTrilinos takes advantage of the flexibility and ease of use of Python, and the efficiency of the underlying C++, C and Fortran numerical kernels. This paper covers recent, previously unpublished advances in the PyTrilinos package.


2007 ◽  
Author(s):  
T. Campbell ◽  
B. de Sonneville ◽  
L. Benedet ◽  
D. J. W. Walstra ◽  
C. W. Finkl

Author(s):  
D.S. Rakisheva ◽  
◽  
B.G. Mukanova ◽  
I.N. Modin ◽  
◽  
...  

Numerical modeling of the problem of dam monitoring by the Electrical Resistivity Tomography method is carried out. The mathematical model is based on integral equations with a partial Fourier transform with respect to one spatial variable. It is assumed that the measurement line is located across the dam longitude. To approximate the shape of the dam surface, the Radial Basic Functions method is applied. The influence of locations of the water-dam, dam-basement, basement-leakage boundaries with respect to the sounding installation, which is partially placed under the headwater, is studied. Numerical modeling is carried out for the following varied parameters: 1) water level at the headwater; 2) the height of the leak; 3) the depth of the leak; 4) position of the supply electrode; 5) water level and leaks positions are changing simultaneously. Modeling results are presented in the form of apparent resistivity curves, as it is customary in geophysical practice.


2015 ◽  
Vol 35 ◽  
pp. 232-235 ◽  
Author(s):  
Leonardo Piccinini ◽  
Paolo Fabbri ◽  
Marco Pola ◽  
Enrico Marcolongo ◽  
Alessia Rosignoli

2016 ◽  
Vol 41 ◽  
pp. 10-13 ◽  
Author(s):  
Luca Alberti ◽  
Martino Cantone ◽  
Silvia Lombi ◽  
Alessandra Piana

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