[cig-commits] r12625 - in doc/cigma/manual: . formats
luis at geodynamics.org
luis at geodynamics.org
Wed Aug 13 13:23:06 PDT 2008
Author: luis
Date: 2008-08-13 13:23:06 -0700 (Wed, 13 Aug 2008)
New Revision: 12625
Added:
doc/cigma/manual/formats/
doc/cigma/manual/formats/file_formats.lyx
Removed:
doc/cigma/manual/formats/file_formats.lyx
Log:
Shorter dirname
Copied: doc/cigma/manual/formats (from rev 12509, doc/cigma/manual/file_formats)
Deleted: doc/cigma/manual/formats/file_formats.lyx
===================================================================
--- doc/cigma/manual/file_formats/file_formats.lyx 2008-08-01 21:44:21 UTC (rev 12509)
+++ doc/cigma/manual/formats/file_formats.lyx 2008-08-13 20:23:06 UTC (rev 12625)
@@ -1,403 +0,0 @@
-#LyX 1.5.6 created this file. For more info see http://www.lyx.org/
-\lyxformat 276
-\begin_document
-\begin_header
-\textclass book
-\begin_preamble
-\newcommand{\mynote}[1]{}
-\end_preamble
-\language english
-\inputencoding auto
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_default_family default
-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-\graphics default
-\paperfontsize default
-\spacing single
-\papersize default
-\use_geometry false
-\use_amsmath 1
-\use_esint 1
-\cite_engine basic
-\use_bibtopic false
-\paperorientation portrait
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\defskip medskip
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\author ""
-\author ""
-\end_header
-
-\begin_body
-
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Standard
-
-
-\backslash
-mynote{}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Chapter
-File Formats
-\end_layout
-
-\begin_layout Standard
-To differentiate between these input and output file formats, you will need
- to provide an appropriate file extension.
- Currently recognized file extensions include
-\family typewriter
-*.h5
-\family default
- for HDF5 files,
-\family typewriter
-*.vtk
-\family default
- for legacy VTK files, and
-\family typewriter
-*.dat
-\family default
- for simple text files.
-\end_layout
-
-\begin_layout Section
-Input File Format
-\end_layout
-
-\begin_layout Standard
-There are five different objects you will want to use as input to Cigma,
- all of which can be represented as two-dimensional datasets.
- These are the
-\end_layout
-
-\begin_layout Itemize
-mesh coordinates
-\end_layout
-
-\begin_layout Itemize
-mesh connectivity
-\end_layout
-
-\begin_layout Itemize
-field coefficients (degrees of freedom)
-\end_layout
-
-\begin_layout Itemize
-quadrature rule points
-\end_layout
-
-\begin_layout Itemize
-quadrature rule weights
-\end_layout
-
-\begin_layout Subsection
-HDF5
-\end_layout
-
-\begin_layout Standard
-HDF5 files are organized in a hierarchical structure, similar to a UNIX
- file system.
- Two types of primary objects, groups and datasets, are stored in this structure.
- A group contains instances of zero or more groups or datasets, while a
- dataset stores a multi-dimensional array of data elements.
- Both kinds of objects are accompanied by supporting metadata known as attribute
-s.
-\end_layout
-
-\begin_layout Standard
-A dataset is physically stored in two parts: a header and a data array.
- The header contains miscellaneous metadata describing the dataset as well
- as information that is needed to interpret the array portion of the dataset.
- Essentially, it includes the name, datatype, dataspace, and storage layout
- of the dataset.
- The name is a text string identifying the dataset.
- The datatype describes the type of the data array elements.
- The dataspace defines the dimensionality of the dataset, i.e., the size and
- shape of the multi-dimensional array.
-\end_layout
-
-\begin_layout Standard
-In Cigma you always provide an explicit path to every dataset, so you have
- a fair amount of flexibility for how you organize your datasets inside
- HDF5 files.
- For example, a typical Cigma HDF5 file could have the following structure.
-\end_layout
-
-\begin_layout LyX-Code
-model.h5
-\end_layout
-
-\begin_layout LyX-Code
-
-\backslash
-__ model
-\end_layout
-
-\begin_layout LyX-Code
- |__ mesh
-\end_layout
-
-\begin_layout LyX-Code
- | |__ coordinates [nno x nsd]
-\end_layout
-
-\begin_layout LyX-Code
- |
-\backslash
-__ connectivity [nel x ndof]
-\end_layout
-
-\begin_layout LyX-Code
-
-\backslash
-__ variables
-\end_layout
-
-\begin_layout LyX-Code
- |__ temperature
-\end_layout
-
-\begin_layout LyX-Code
- | |__ step00000 [nno x 1]
-\end_layout
-
-\begin_layout LyX-Code
- | |__ step00010 [nno x 1]
-\end_layout
-
-\begin_layout LyX-Code
- |
-\backslash
-...
-\end_layout
-
-\begin_layout LyX-Code
- |__ displacement
-\end_layout
-
-\begin_layout LyX-Code
- | |__ step00000 [nno x 3]
-\end_layout
-
-\begin_layout LyX-Code
- | |__ step00010 [nno x 3]
-\end_layout
-
-\begin_layout LyX-Code
- |
-\backslash
-...
-\end_layout
-
-\begin_layout LyX-Code
-
-\backslash
-__ velocity
-\end_layout
-
-\begin_layout LyX-Code
- |__ step00000 [nno x 3]
-\end_layout
-
-\begin_layout LyX-Code
- |__ step00010 [nno x 3]
-\end_layout
-
-\begin_layout LyX-Code
-
-\backslash
-...
-\end_layout
-
-\begin_layout Standard
-Generally, Cigma will only require you to specify the path to a specific
- field dataset.
- If a small amount of metadata is present in your field dataset, the rest
- of the required information, such as which mesh and finite elements to
- use, will be deduced from that metadata.
-\end_layout
-
-\begin_layout Description
-MeshID an identifier assigned for use in linking child datasets to their
- parent mesh.
-\end_layout
-
-\begin_layout Description
-MeshLocation points to the HDF5 group which contains the appropriate coordinates
- and connectivity datasets.
-\end_layout
-
-\begin_layout Description
-FunctionSpace string identifier to determine which shape functions to use
- for interpolating values inside the element (e.g., tet4, hex8, quad4, tri3,
- ...).
-\end_layout
-
-\begin_layout Description
-DatasetType string identifier for classifying the type of data contained
- in the dataset (e.g., points, connectivity, degrees of freedom, quadrature
- rules, global quadrature points, global field values).
-\end_layout
-
-\begin_layout Subsection
-VTK
-\end_layout
-
-\begin_layout Standard
-The current version of Cigma only supports VTK unstructured grid datasets
- of a single element type.
- You can still compare various unstructured grids with different element
- types to each other.
-\end_layout
-
-\begin_layout Standard
-Note that while you typically provide a path (or name) for every dataset,
- this is not necessary when specifying a VTK mesh, since this data is taken
- from the special Points and Cells arrays, which you cannot rename.
- However, you will still need to provide a name when referring to the field
- coefficients, which are assumed to be stored as Point Data in the input
- VTK file.
-\end_layout
-
-\begin_layout Standard
-For more information, you may want to refer to Visualization ToolKit's
-\begin_inset LatexCommand htmlurl
-name "File Formats"
-target "www.vtk.org/pdf/file-formats.pdf"
-
-\end_inset
-
- document.
-
-\end_layout
-
-\begin_layout Subsection
-Text
-\end_layout
-
-\begin_layout Standard
-The text format is always in table form, with the dimensions of the table
- specified in the first line.
- For example, mesh coordinates can be specified in the following format
-\end_layout
-
-\begin_layout LyX-Code
-<nno> <nsd>
-\end_layout
-
-\begin_layout LyX-Code
-x1 y1 z1
-\end_layout
-
-\begin_layout LyX-Code
-x2 y2 z2
-\end_layout
-
-\begin_layout LyX-Code
-x3 y3 z3
-\end_layout
-
-\begin_layout LyX-Code
-...
-\end_layout
-
-\begin_layout Standard
-Mesh connectivity with
-\end_layout
-
-\begin_layout LyX-Code
-nel ndofs
-\end_layout
-
-\begin_layout LyX-Code
-node_1 node_2 node_3 node_4 ...
-\end_layout
-
-\begin_layout LyX-Code
-node_1 node_2 node_3 node_4 ...
-\end_layout
-
-\begin_layout LyX-Code
-node_1 node_2 node_3 node_4 ...
-\end_layout
-
-\begin_layout LyX-Code
-...
-\end_layout
-
-\begin_layout Standard
-A generic field with
-\family typewriter
-ndim
-\family default
- components (i.e., scalar, vector, or tensor) is specified by
-\end_layout
-
-\begin_layout LyX-Code
-num ndim
-\end_layout
-
-\begin_layout LyX-Code
-f1 f2 f3 ..
-\end_layout
-
-\begin_layout LyX-Code
-f1 f2 f3 ..
-\end_layout
-
-\begin_layout LyX-Code
-...
-\end_layout
-
-\begin_layout Standard
-In this last case, the number of rows could refer to either
-\family typewriter
-nno
-\family default
- or
-\family typewriter
-nel
-\family default
-, depending on whether the field is node-based or cell-based.
-\end_layout
-
-\begin_layout Section
-Output File Format
-\end_layout
-
-\begin_layout Standard
-The output format for residuals consists simply of a list of scalars for
- each element in the discretization.
- If you specify a
-\family typewriter
-.vtk
-\family default
- extension for your output file, this will result in an scalar dataset named
- epsilon stored using the legacy VTK file format in the Cell Data section
- of the output file.
- Note that this output consists of the squared values of the local residuals,
- so further post-processing will be necessary.
-\end_layout
-
-\end_body
-\end_document
Copied: doc/cigma/manual/formats/file_formats.lyx (from rev 12624, doc/cigma/manual/file_formats/file_formats.lyx)
===================================================================
--- doc/cigma/manual/formats/file_formats.lyx (rev 0)
+++ doc/cigma/manual/formats/file_formats.lyx 2008-08-13 20:23:06 UTC (rev 12625)
@@ -0,0 +1,1098 @@
+#LyX 1.5.5 created this file. For more info see http://www.lyx.org/
+\lyxformat 276
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+\newcommand{\mynote}[1]{}
+\end_preamble
+\language english
+\inputencoding auto
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+\graphics default
+\paperfontsize default
+\spacing single
+\papersize default
+\use_geometry false
+\use_amsmath 1
+\use_esint 1
+\cite_engine basic
+\use_bibtopic false
+\paperorientation portrait
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\defskip medskip
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\author ""
+\author ""
+\end_header
+
+\begin_body
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+mynote{
+\end_layout
+
+\begin_layout Standard
+
+TODO: Rename file_formats.lyx to formats.lyx
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+Define the dimensions for every object in the file (summarize only the tables
+ in the appendix)
+\end_layout
+
+\begin_layout Standard
+
+ Mesh Coordinates
+\end_layout
+
+\begin_layout Standard
+
+ Mesh Connectivity (list of Element Blocks)
+\end_layout
+
+\begin_layout Standard
+
+ Field Variables (Global, Nodal, Element)
+\end_layout
+
+\begin_layout Standard
+
+ Element Tabulation (Shape function, Shape Function Derivatives)
+\end_layout
+
+\begin_layout Standard
+
+ Integration Rule (Weights and Local Points)
+\end_layout
+
+\begin_layout Standard
+
+ Global Integration Points
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+Explain structure of each file format:
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ Text Format
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ All arrays specified explicitly in several text files containing a list
+ of floating point numbers.
+\end_layout
+
+\begin_layout Standard
+
+ The first two numbers indicate the dimensions of the array, followed
+ by a list of floats
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ --integration-mesh-coordinates=imesh_coords.dat
+\end_layout
+
+\begin_layout Standard
+
+ --integration-mesh-connectivity=imesh_connect.dat
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ --integration-rule-points=tet4_order10_points.dat
+\end_layout
+
+\begin_layout Standard
+
+ --integration-rule-weights=tet4_order10_weights.dat
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ --first-mesh-coordinates=first_coords.dat
+\end_layout
+
+\begin_layout Standard
+
+ --first-mesh-connectivity=first_connect.dat
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ --second-mesh-coordinates=first_coords.dat
+\end_layout
+
+\begin_layout Standard
+
+ --second-mesh-connectivity=first_connect.dat
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ --first-dofs=first_var_stepN.dat
+\end_layout
+
+\begin_layout Standard
+
+ --second-dofs=second_var_stepN.dat
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ --integration-rule=tet4_order10.dat <-- (weights in first column)
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ Simple Arrays (HDF5)
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ Structure of Model Definition
+\end_layout
+
+\begin_layout Standard
+
+ root group at /model
+\end_layout
+
+\begin_layout Standard
+
+ mesh data at /model/mesh
+\end_layout
+
+\begin_layout Standard
+
+ node coordinates as specified on global coordinate system at /model/mesh
+/coordinates
+\end_layout
+
+\begin_layout Standard
+
+ list of element blocks at /model/mesh/connectivity
+\end_layout
+
+\begin_layout Standard
+
+ note that each element block is tagged by element type in the FE
+ attribute
+\end_layout
+
+\begin_layout Standard
+
+ degrees-of-freedom data
+\end_layout
+
+\begin_layout Standard
+
+ organized by variable at /model/vars/var, or even just /model/var
+\end_layout
+
+\begin_layout Standard
+
+ list of steps: /model/var/step{0,1,...,N}
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ Structure of file defining an Integration Rule
+\end_layout
+
+\begin_layout Standard
+
+ root group is / by default, but may be specified directly (eg, as
+ /rule)
+\end_layout
+
+\begin_layout Standard
+
+ root group is tagged with FE string indicating the source element
+ (tet4, ...)
+\end_layout
+
+\begin_layout Standard
+
+ integration points contained at /rule/points
+\end_layout
+
+\begin_layout Standard
+
+ integration points contained at /rule/weights
+\end_layout
+
+\begin_layout Standard
+
+ Structure of file with Residuals
+\end_layout
+
+\begin_layout Standard
+
+ root group is / by default, but it must exist if specified
+\end_layout
+
+\begin_layout Standard
+
+
+\end_layout
+
+\begin_layout Standard
+
+ VTK
+\end_layout
+
+\begin_layout Standard
+
+ Basic structure:
+\end_layout
+
+\begin_layout Standard
+
+ VTK Grid
+\end_layout
+
+\begin_layout Standard
+
+ VTK Dataset consists of the mesh information (node coordinates
+ and associated connectivity relations)
+\end_layout
+
+\begin_layout Standard
+
+ VTK Data Arrays come in two types (Point Data and Cell Data)
+\end_layout
+
+\begin_layout Standard
+
+ VTK Point Data - scalars, vectors, tensors as defined on the
+ nodes
+\end_layout
+
+\begin_layout Standard
+
+ VTK Cell Data - scalars, vectors, tensors as defined on each
+ element
+\end_layout
+
+\begin_layout Standard
+
+ Structure of different types
+\end_layout
+
+\begin_layout Standard
+
+ Unstructured Grid
+\end_layout
+
+\begin_layout Standard
+
+ mesh points: given explicitly in a simple array
+\end_layout
+
+\begin_layout Standard
+
+ mesh connectivity: given explicitly in a list of simple arrays
+\end_layout
+
+\begin_layout Standard
+
+ element types: Line, Quad, Tetra, Hexahedron, Quadratic Triangle,
+ Quadratic Quad, Quadratic Tetra, Quadratic Hexahedron
+\end_layout
+
+\begin_layout Standard
+
+ Structured Grid
+\end_layout
+
+\begin_layout Standard
+
+ mesh points: given explicitly in a simple array
+\end_layout
+
+\begin_layout Standard
+
+ mesh connectivity: derived from dimensions (nx, ny, nz)
+\end_layout
+
+\begin_layout Standard
+
+ element types: Quad, Pixel, Hex, Voxel
+\end_layout
+
+\begin_layout Standard
+
+ Rectilinear Grid
+\end_layout
+
+\begin_layout Standard
+
+ mesh dimensions: (nx, ny, nz)
+\end_layout
+
+\begin_layout Standard
+
+ mesh points: derived from 'double xcoords[nx], ycoords[ny], zcoords[n
+z]' arrays
+\end_layout
+
+\begin_layout Standard
+
+ element types: Pixel, Voxel
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ UCD
+\end_layout
+
+\begin_layout Standard
+
+ Format described in (LINK-TO-DOCUMENT).
+\end_layout
+
+\begin_layout Standard
+
+ Using VTK API (vtkAVSucdReader) to read (*.inp) files
+\end_layout
+
+\begin_layout Standard
+
+ Just extracts the data into an Unstructured Grid
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+ ExodusII
+\end_layout
+
+\begin_layout Standard
+
+ This type of mesh can be generated by other programs, such as CUBIT
+\end_layout
+
+\begin_layout Standard
+
+ Currently only used to specify an integration mesh, but it is capable
+ of storing degree-of-freedom data as well.
+\end_layout
+
+\begin_layout Standard
+
+ Utility script for converting *.exo into the appropriate *.h5 file (need
+ PyTables, Numpy, Scientific.IO.NetCDF)
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+--------------
+\end_layout
+
+\begin_layout Standard
+
+From running.lyx:
+\end_layout
+
+\begin_layout Standard
+
+The underlying data storage format for Cigma is the HDF5 format, due to
+ its flexibility for storing and organizing large amounts of data.
+ The Hierarchical Data Format (HDF) is designed for storing, retrieving,
+ analyzing, visualizing, and converting scientific data.
+ It uses a hierarchical structure that provides users a host of options
+ for organizing how their data is stored in HDF5 files.
+ Using HDF5 datasets in Cigma allows us to avoid having to convert between
+ too many distinct formats.
+ Moreover, due to the amount of disk I/O, large finite element meshes can
+ be handled more efficiently in binary format.
+
+\end_layout
+
+\begin_layout Standard
+
+Another popular format for providing mesh and field inputs.You can easily
+ examine the structure of an input file by using the cigma list command,
+ which will simply reveal the names and dimensions of all datasets inside
+ the specified file.
+\end_layout
+
+\begin_layout Standard
+
+Inputs can be either HDF5 or VTK.
+ Specifying the complete path to a dataset consists of the special form
+ filepath:dataset, a colon-delimited pair of file path and dataset path.
+\end_layout
+
+\begin_layout Standard
+
+Mesh inputs are currently only unstructured grids.
+\end_layout
+
+\begin_layout Standard
+
+Only exception are the residuals, which are written in legacy VTK format
+ as scalar cell data over an unstructured grid.
+\end_layout
+
+\begin_layout Standard
+
+Because Cigma relies on the ability of the user to specify dataset paths,
+ we have provided a command called list for viewing the structure of an
+ input file.
+ Its usage is very simple.
+
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+This chapter may be summarized by simply stating that most input data can
+ be specified as a two-dimensional array.
+ The meaning of this array, of course, is dependent on context.
+ That is the main concept that we have to get accross in this chapter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Chapter
+Data and File Formats
+\end_layout
+
+\begin_layout Standard
+As we've seen in the previous chapters, there are a number of data objects
+ involved in making any particular comparison.
+ Here, we discuss the variety of formats available, as well as the layout
+ within the corresponding data file.
+\end_layout
+
+\begin_layout Section
+Data Formats
+\end_layout
+
+\begin_layout Standard
+The basic data structure is a two-dimensional array of values, stored in
+
+\newline
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Array shape
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $(m,n)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Array Data
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $a_{11},a_{12},\ldots,a_{1n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $a_{21},a_{22},\ldots,a_{2n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\cdots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $a_{m1},a_{m2},\ldots,a_{mn}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Mesh
+\end_layout
+
+\begin_layout Subsection
+Field Variables
+\end_layout
+
+\begin_layout Subsection
+Integration Rule
+\end_layout
+
+\begin_layout Subsection
+Integration Points and Values
+\end_layout
+
+\begin_layout Subsection
+Spherical Harmonics
+\end_layout
+
+\begin_layout Section
+File Formats
+\end_layout
+
+\begin_layout Section
+Input Files
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+There are five different objects you will want to use as input to Cigma,
+ all of which can be represented as two-dimensional datasets.
+ These are the
+\end_layout
+
+\begin_layout Itemize
+mesh coordinates
+\end_layout
+
+\begin_layout Itemize
+mesh connectivity
+\end_layout
+
+\begin_layout Itemize
+field coefficients (degrees of freedom)
+\end_layout
+
+\begin_layout Itemize
+quadrature rule points
+\end_layout
+
+\begin_layout Itemize
+quadrature rule weights
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Now that we have examined what kinds of objects we will be accessing, let's
+ discuss the actual layout.
+\end_layout
+
+\begin_layout Subsection
+HDF5
+\end_layout
+
+\begin_layout Standard
+HDF5 files are organized in a hierarchical structure, similar to a UNIX
+ file system.
+ Two types of primary objects, groups and datasets, are stored in this structure.
+ A group contains instances of zero or more groups or datasets, while a
+ dataset stores a multi-dimensional array of data elements.
+ Both kinds of objects are accompanied by supporting metadata known as attribute
+s.
+\end_layout
+
+\begin_layout Standard
+A dataset is physically stored in two parts: a header and a data array.
+ The header contains miscellaneous metadata describing the dataset as well
+ as information that is needed to interpret the array portion of the dataset.
+ Essentially, it includes the name, datatype, dataspace, and storage layout
+ of the dataset.
+ The name is a text string identifying the dataset.
+ The datatype describes the type of the data array elements.
+ The dataspace defines the dimensionality of the dataset, i.e., the size and
+ shape of the multi-dimensional array.
+\end_layout
+
+\begin_layout Standard
+In Cigma you may always provide an explicit path to every dataset, so you
+ have a fair amount of flexibility for how you organize your datasets inside
+ HDF5 files.
+ For example, a typical Cigma HDF5 file could have the following structure.
+
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Mention these assumptions in the corresponding section in running.lyx
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout LyX-Code
+model.h5
+\end_layout
+
+\begin_layout LyX-Code
+
+\backslash
+__ model
+\end_layout
+
+\begin_layout LyX-Code
+ |__ mesh
+\end_layout
+
+\begin_layout LyX-Code
+ | |__ coordinates [nno x nsd]
+\end_layout
+
+\begin_layout LyX-Code
+ |
+\backslash
+__ connectivity [nel x ndof]
+\end_layout
+
+\begin_layout LyX-Code
+
+\backslash
+__ variables
+\end_layout
+
+\begin_layout LyX-Code
+ |__ temperature
+\end_layout
+
+\begin_layout LyX-Code
+ | |__ step00000 [nno x 1]
+\end_layout
+
+\begin_layout LyX-Code
+ | |__ step00010 [nno x 1]
+\end_layout
+
+\begin_layout LyX-Code
+ |
+\backslash
+...
+\end_layout
+
+\begin_layout LyX-Code
+ |__ displacement
+\end_layout
+
+\begin_layout LyX-Code
+ | |__ step00000 [nno x 3]
+\end_layout
+
+\begin_layout LyX-Code
+ | |__ step00010 [nno x 3]
+\end_layout
+
+\begin_layout LyX-Code
+ |
+\backslash
+...
+\end_layout
+
+\begin_layout LyX-Code
+
+\backslash
+__ velocity
+\end_layout
+
+\begin_layout LyX-Code
+ |__ step00000 [nno x 3]
+\end_layout
+
+\begin_layout LyX-Code
+ |__ step00010 [nno x 3]
+\end_layout
+
+\begin_layout LyX-Code
+
+\backslash
+...
+\end_layout
+
+\begin_layout Standard
+Generally, Cigma will only require you to specify the path to a specific
+ field dataset.
+ If a small amount of metadata is present in your field dataset, the rest
+ of the required information, such as which mesh and finite elements to
+ use, will be deduced from that metadata.
+\end_layout
+
+\begin_layout Description
+MeshID an identifier assigned for use in linking child datasets to their
+ parent mesh.
+\end_layout
+
+\begin_layout Description
+MeshLocation points to the HDF5 group which contains the appropriate coordinates
+ and connectivity datasets.
+\end_layout
+
+\begin_layout Description
+FunctionSpace string identifier to determine which shape functions to use
+ for interpolating values inside the element (e.g., tet4, hex8, quad4, tri3,
+ ...).
+\end_layout
+
+\begin_layout Description
+DatasetType string identifier for classifying the type of data contained
+ in the dataset (e.g., points, connectivity, degrees of freedom, quadrature
+ rules, global quadrature points, global field values).
+\end_layout
+
+\begin_layout Subsection
+VTK
+\end_layout
+
+\begin_layout Standard
+The current version of Cigma only supports VTK unstructured grid datasets
+ of a single element type.
+ You can still compare various unstructured grids with different element
+ types to each other.
+\end_layout
+
+\begin_layout Standard
+Note that while you typically provide a path (or name) for every dataset,
+ this is not necessary when specifying a VTK mesh, since this data is taken
+ from the special Points and Cells arrays, which you cannot rename.
+ However, you will still need to provide a name when referring to the field
+ coefficients, which are assumed to be stored as Point Data in the input
+ VTK file.
+\end_layout
+
+\begin_layout Standard
+For more information, you may want to refer to Visualization ToolKit's
+\begin_inset LatexCommand htmlurl
+name "File Formats"
+target "www.vtk.org/pdf/file-formats.pdf"
+
+\end_inset
+
+ document.
+
+\end_layout
+
+\begin_layout Subsection
+Text
+\end_layout
+
+\begin_layout Standard
+The text format is always in table form, with the dimensions of the table
+ specified in the first line.
+ For example, mesh coordinates can be specified in the following format
+\end_layout
+
+\begin_layout LyX-Code
+<nno> <nsd>
+\end_layout
+
+\begin_layout LyX-Code
+x1 y1 z1
+\end_layout
+
+\begin_layout LyX-Code
+x2 y2 z2
+\end_layout
+
+\begin_layout LyX-Code
+x3 y3 z3
+\end_layout
+
+\begin_layout LyX-Code
+...
+\end_layout
+
+\begin_layout Standard
+Mesh connectivity with
+\end_layout
+
+\begin_layout LyX-Code
+nel ndofs
+\end_layout
+
+\begin_layout LyX-Code
+node_1 node_2 node_3 node_4 ...
+\end_layout
+
+\begin_layout LyX-Code
+node_1 node_2 node_3 node_4 ...
+\end_layout
+
+\begin_layout LyX-Code
+node_1 node_2 node_3 node_4 ...
+\end_layout
+
+\begin_layout LyX-Code
+...
+\end_layout
+
+\begin_layout Standard
+A generic field with
+\family typewriter
+ndim
+\family default
+ components (i.e., scalar, vector, or tensor) is specified by
+\end_layout
+
+\begin_layout LyX-Code
+num ndim
+\end_layout
+
+\begin_layout LyX-Code
+f1 f2 f3 ..
+\end_layout
+
+\begin_layout LyX-Code
+f1 f2 f3 ..
+\end_layout
+
+\begin_layout LyX-Code
+...
+\end_layout
+
+\begin_layout Standard
+In this last case, the number of rows could refer to either
+\family typewriter
+nno
+\family default
+ or
+\family typewriter
+nel
+\family default
+, depending on whether the field is node-based or cell-based.
+\end_layout
+
+\begin_layout Section
+Output File
+\end_layout
+
+\begin_layout Standard
+Depending on the particular operation you perform, there are three different
+ kinds of output files.
+ The output format for residuals consists simply of a list of scalars for
+ each element in the discretization.
+ If you specify a
+\family typewriter
+.vtk
+\family default
+ extension for your output file, this will result in an scalar dataset named
+ epsilon stored using the legacy VTK file format in the Cell Data section
+ of the output file.
+ Note that this output consists of the squared values of the local residuals,
+ so further post-processing will be necessary.
+\end_layout
+
+\end_body
+\end_document
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