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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3 % Copyright (c) 2003-2012 by University of Queensland
4 % http://www.uq.edu.au
5 %
6 % Primary Business: Queensland, Australia
7 % Licensed under the Open Software License version 3.0
8 % http://www.opensource.org/licenses/osl-3.0.php
9 %
10 % Development until 2012 by Earth Systems Science Computational Center (ESSCC)
11 % Development since 2012 by School of Earth Sciences
12 %
13 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
15 \section{Why \esc?}
16 \esc is a scripting environment for mathematical modelling based on partial
17 differential equations (PDEs). It provides a high-level of abstraction from the
18 underlying numerical schemes and their implementations. By freeing the user from
19 considerations like data constructs, meshing and parallelisation, the user can
20 concentrate on the modelling aspects of the problem and still properly utilise
21 the powerful mathematical capabilities of PDEs.
23 \esc is built upon the interpreted programming language \pyt\footnote{see
24 \url{www.python.org}}, a scripting language with many intrinsic functions and
25 capabilities. Additionally, there are also a large number of software packages
26 for \pyt which can be used in conjunction with \esc. These packages include
27 functions and data constructs for linear algebra, statistics, visualisation,
28 image processing and data plotting among others. Furthermore, most \esc scripts
29 are scalable and able to run on single core desktop computers right through to
30 multi-core supercomputers\footnote{\esc supports distributed memory
31 architectures with multi-core processors through MPI and threading. See the \esc
32 user guide at \url{https://launchpad.net/escript-finley/+download} for details.}
33 with no modifications to the scripts.
35 There are many benefits for using a software platform like \esc for projects
36 that involve mathematical modelling. Building on top of an existing environment
37 such as \esc is in many cases much simpler and more cost effective than
38 building an original implementation from the ground up. A modelling environment
39 needs data structures and solution algorithms which take time to develop and
40 test properly, \esc has already covered these aspects and its implementation
41 has been widely tested for bugs. Although existing environments may not provide
42 the user with the fastest algorithms for their problems, it is generally the
43 case, that the overall time needed to identify, implement and test the optimal
44 algorithm will exceed the time needed to implement and solve the problem with
45 pre-developed and tested software. This is particularly true if a simulation
46 does not need to be executed repetitively, or has relatively short lifetime.
47 A model for a publication or thesis would be one such instance.
49 When it comes to solving partial differential equations, \esc is ideal as it is
50 especially designed for this task. Other implementations are merely an add-on to
51 a linear algebra focused system (\textit{e.g.} MATLAB). The \esc approach gives
52 the user a cleaner environment to work with and provides better efficiency when
53 dealing with PDE coefficients. Data structures in \esc allow the user to
54 abstract away details such as data types of these coefficients. For example, if
55 a model has been tested with a constant PDE coefficient then the unchanged
56 script can be run with variable coefficients from a database or as a function of
57 a dependent variable. This capability of \esc is possible because \esc uses the
58 language of PDEs (as opposed to linear algebra) to describe a model. As it turns
59 out, the \esc approach can be applied efficiently in very large software
60 projects as it leads to a clearer structure for the code, by separating
61 modelling issues from low-level numerical and computational performance issues.
62 At the same time, this arrangement also allows for the implementation of complex
63 model coupling on a higher-level.
65 The use of \pyt as the platform for \esc makes the development of models simple
66 from a user perspective, as \pyt is intuitive and easy to learn. This simplicity
67 does not hamper experienced users either as \pyt also provides access to a very
68 large number of tools. This makes it an attractive environment to work in. Best
69 of all, \esc is released under an open software license and is freely available
70 for download.
72 \section{How to use this Cookbook}
73 This manual is written with the intention of giving new users a practical
74 introduction to \esc. It demonstrates how to solve a variety of problems from
75 simple to advanced. We recommend that new users work through the
76 \textit{first few sets of examples} in Chapters \ref{CHAP HEAT DIFF},
77 \ref{CHAP HEAT 2a} and \ref{CHAP HEAT 2}).
78 These chapters contain the necessary basic knowledge, and explain some of the
79 common aspects and modules of \esc. The simple examples demonstrate how to
80 create, solve and visualise PDE based models.
81 Future chapters (as they are added to this tutorial) will cover more advanced
82 topics with more complex models and methods. Further examples are available in
83 the \esc user guide.
85 All examples covered in this cookbook have been scripted and are ready to run.
86 They are available from the \exf folder in the \esc directory. These scripts
87 provide a basis for users to develop their own models while at the same time
88 demonstrating the steps required to completely solve and visualise the PDE
89 problems.
91 % All of the examples in this cookbook have been developed on a Linux based
92 % operating system.
93 % Unfortunately Windows and Mac support cannot be guaranteed. However, in most
94 % cases minor modifications to the scripts will generally solve any problems.
96 \input{quickstart}
97 \input{escpybas}

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