


 Krylov space solver in Fortran 2009: Beta version  

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A geophysicist understands and/or approximates how a given set
of earth properties (model) would create a given set of measurements (data). Geophysics
is often an attempt to do the inverse: from a
set of recorded data, estimate a model.
When the set of measurements and/or the number of model points is large, matrixbased
approaches become impractical. Iterative approaches are often the
method of choice for largescale estimation problems. Iterative solvers can become
quite complex and are generally more the domain of the mathematician
than the geophysicist. Ideally we would like to leverage the mathematician's expertise
without having to understand all of the details of the implementation.
Gockenbach (1994); Nichols et al. (1993)
all implemented
model estimation through an objectoriented framework, allowing this separation
using
C++. Schwab (1998) described a javabased approach to this problem, and
Clapp (2005)
described a pythonbased approach for large, outofcore solvers. SEP chose
instead to use Fortran 90. Unfortunately, Fortran 90 is far from a complete
objectoriented language, and as a result complicated inversion problems are
cumbersome to describe given its limitations. The problems
encountered in
implementing
the hybrid norm (Zhang and Claerbout, 2010; Claerbout, 2009) is but one example of the
limitations
of Fortran 90 for solving inverse problems. Recently, Fortran compilers
have begun to support Fortran's latest incarnation, Fortran 2008, a more
complete implementation of the needed object oriented constructs. This paper is a follow up to
Clapp (2010),
which described how an implementation could be done in Fortran 2003, but was hampered
by the immaturity of the Fortran compiler.
In this paper, I show the implementation of an abstract solver class in Fortran 2008.
I begin by describing one method to implement an abstract operatorbased iterative solver.
I describe an abstract vector, abstract operator, and solver class.
I finish by showing how a small geophysical inverse problems can be solved using these classes
and concrete classes inherited from them.



 Krylov space solver in Fortran 2009: Beta version  

Next: Operatorbased objectoriented solvers
Up: Krylov space solver in
Previous: Krylov space solver in
20110913