# Diff of /trunk/doc/user/ripley.tex

revision 5692 by jfenwick, Wed Jun 17 23:39:18 2015 UTC revision 5693 by sshaw, Fri Jun 26 01:13:47 2015 UTC
# Line 41  available. Consider the following exampl Line 41  available. Consider the following exampl
41   dom = Rectangle(9, 9)   dom = Rectangle(9, 9)
42  \end{python}  \end{python}
43
44    Multi-resolution domains are supported in \ripley via use of \class{MultiBrick}
45    and \class{MultiRectangle}. Each level of one of
46    these domains has twice the elements in each axis of the next lower resolution.
47    The \class{MultiBrick} is not currently supported when running \escript with
48    multiple processes using \MPI. Interpolation between these multi-resolution
49    domains is possible providing they have matching dimensions and subdivisions,
50    along with a compatible number of elements. To simplify these conditions the
51    use of \class{MultiResolutionDomain} is highly recommended. The following
52    example creates two 2D domains of different resolutions and interpolates
53    between them:
54
55    \begin{python}
56     from esys.ripley import MultiResolutionDomain
57     mrd = MultiResolutionDomain(2, n0=10, n1=10)
58     ten_by_ten = mrd.getLevel(0)
59     data10 = Vector(..., Function(ten_by_ten))
60     ...
61     forty_by_forty = mrd.getLevel(2)
62     data40 = interpolate(data10, Function(forty_by_forty))
63    \end{python}
64
65  \section{Formulation}  \section{Formulation}
66  For a single PDE that has a solution with a single component the linear PDE is  For a single PDE that has a solution with a single component the linear PDE is
67  defined in the following form:  defined in the following form:
# Line 124  case the coordinates will range between Line 145  case the coordinates will range between
145  bottom-left node is located at $(5.5, 9.0)$ and the top-right node has  bottom-left node is located at $(5.5, 9.0)$ and the top-right node has
146  coordinates $(15.5, 14.0)$, see Figure~\ref{fig:ripleyrect}.  coordinates $(15.5, 14.0)$, see Figure~\ref{fig:ripleyrect}.
147
148    The \class{MultiResolutionDomain} class is available as a wrapper, taking the
149    dimension of the domain followed by the same arguments as \class{Brick} (if
150    a two-dimensional domain is requested, any extra arguments over those used by
151    \class{Rectangle} are ignored). All of these standard arguments to
152    \class{MultiResolutionDomain} must be supplied as keyword arguments
153    (e.g. \var{d0}=...). The \class{MultiResolutionDomain} can then generate
154    compatible domains for interpolation.
155
156  \section{Linear Solvers in \SolverOptions}  \section{Linear Solvers in \SolverOptions}
157  Currently direct solvers and GPU-based solvers are not supported under \MPI  Currently direct solvers and GPU-based solvers are not supported under \MPI
158  when running with more than one rank.  when running with more than one rank.
# Line 137  ill-posed equations, \ripley uses the \M Line 166  ill-posed equations, \ripley uses the \M
166  non-regular \MKL may return without a proper error code. If you observe  non-regular \MKL may return without a proper error code. If you observe
167  suspicious solutions when using \MKL, this may be caused by a non-invertible  suspicious solutions when using \MKL, this may be caused by a non-invertible
168  operator.} solver package. If \MKL is not available \UMFPACK is used.  operator.} solver package. If \MKL is not available \UMFPACK is used.
169  If \UMFPACK is not available a suitable iterative solver from \PASO is used.  If \UMFPACK is not available a suitable iterative solver from \PASO is used, but
170    if a direct solver was requested via the \SolverOptions an exception will be
171    raised.
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