Glossary of terms used in Mozart

Author: Philippe Fullsack [PF]

Edited and updated by Bonny Lee [BL]


Last update: August 29, 2003

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A-node -- (A-NODE)
[PF] Refers to a node whose points belong to a algebraic system of equations to be solved

See also: Node

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boundary conditions
Refers to

See also: PDE-type

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constraints
See also: Penalization

Comm -- (STRUCTURE CLASS for : Communication)
See also: Parallelism

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domain decomposition
See also: Uzawa
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Graph -- (STRUCTURE CLASS for : Graphs)
See also: Structure

grid
[definition needed here..]
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interface
[PF] A line (in 2d, surface in 3d) which separates 2 regions of space . In our applications, represented either fuzzily by a cloud of points, or by a piecewise linear or polynomial (cubic splines) 1d embedding. Usage: interfaces are typically used as a common border to regions which differ in SOME aspect (e.g. mesh grading of material color) OR as a representation of an object immersed in a (homogeneous or not) region. In the latter case the object itself 'carries the difference'. OR interfaces may be used to partition space for whatever purpose..

See also: nodeline

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Lsystem-- (STRUCTURE CLASS for : linear (or matrix-) systems )
See also: Structure

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Media
[PF] Refers to intrinsic properties of a system which takes the form of a set of relations between various subsets of a system state
Media is an extension of the concept of 'lois constitutives' (behaviour law?) used in continuum mechanics.
Particular media are : rheologies, thermologies, densitologies, fologies, where the prefix before '-logies' is evocative of which pair of variables are linked
In the context of continuum mechanics or thermodynamics relations occur primarily as :
Mozart refers to X-Media where the prefix X is a mnemonic for the type of problem under consideration. (e.g. ADP-Media or T-Media for Advection-diffusion-production systems, or VF-media for viscous fluid systems)

See also: Imports , Polar fluids , Viscoplasticity

Mesh -- (STRUCTURE CLASS for : meshes, set-covers ..)
[PF] Refers to the structure class used to define and manipulate 'meshes'. More specifically a Mesh is a set of entities called elements. They typically correspond to subdomains in a geometric embedding.
Grids may be represented in Mozart as a (Node, Mesh) couple; but meshes may also describe set coverings which may correspond to no grid.
For example a Mesh may be used to represent a tiling of Voronoi cells (dual to the Delaunay triangulation of a Node) or a set of 'patches' with arbitrary overlap.
Such covers are useful in both the so-called meshless methods and in bubble meshing algorithms
Mozart provides several functions for mesh-ing a node into a grid. Several meshers have been developed specifically for Mozart (Quadtree, Octree, Halfner, TensorProduct) , and Jonathan Shewchuk 's exquisite TRIANGLE mesher has been interfaced to Mozart

MPI
[BL] Message Passing Interface standard. "Message passing" is one method of communication among processors in a parallel computer. See http://www-unix.mcs.anl.gov/mpi/index.html.

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Node
[PF] (STRUCTURE CLASS for : clouds, abstract arrays)

[BL] A data structure which represents a cloud of particles. This can be confusing since the term "node" may also be used in the finite element sense as well. To avoid confusion, I try to use the term "Pnode" to mean Philippe's data structure.

See also: A-node, I-node

nodeline
[BL] A data structure consisting of a 1-dimensional array of nodes (particles), or a collection of 1-dimensional arrays of nodes (particles). This is often used to represent an interface or set of interfaces.

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OMP, OpenMP
[BL] A standard specification for a library of routines for shared-memory parallel programming. See www.openmp.org.

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parallel computing
[BL] "Parallel computing is the use of two or more processors (computers) in combination to solve a single problem." Q.F. Stout, "Parallel Computing" at http://www.eecs.umich.edu/~qstout/parallel.html (an amusing introductory explanation of parallel computing).

PDE-type
[PF] To attempt a classification of partial differential equations is a complex story. Broadly speaking , once you have converted the (system of) PDE's to an explicit form (if the system was initially presented as a set of functional equations in the jets), you are left with the biggest distinction: is it or not linear.
If it is linear , and if the space under consideration is a homogeneous space, that is the quotient of 2 Lie groups G/H there is a theory like Fourier's theory to solve those beasts. This is where characters, and representations and Helgason and Kirillov etc come..
By using the fact that Fourier maps convolution to products you are left woth a special algebraic object called the symbol. This (for PDE's on fibre bundles over riemannian spaces) is a matrix section on the cotangent bundle. OK fine no more big words.
Classifying these (symbol) matrices classifies the PDES. E.g. do we have 'nontrivial propagation (that is characteristics, or real eigenvectors) or not (hyperbolic/elliptical distinction)
In the applications tackled in Mozart , some fields obey hyperbolic, other , elliptical type PDES..
We should not think that the (mathematical) game is over. The elliptical case seems to be the best understood but many questions remain opened on the complement..
See also: Scalar products

PESSL
Parallel Engineering and Scientific Subroutine Library. IBM software package for RS/6000 and pSeries computers.

Plot -- (STRUCTURE CLASS for : plots, drawings, X-windows)
See also: A-node, I-node

Pnode
See Node.

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quadrature -- (Integration / summation)
[PF] Refers to the computation of integrals with respect to some measure (e.g. the Lebesgue measure, measures that are absolutely continous with respect to the latter, Stieljes measures, etc..).
Quadrature offers a way to replace infinite systems by discrete ones. For particular systems (e.g. those considered in mechanics) , integrals are invariants conserved by the (Lie group of symmetry of the) flow
Weak formulations of partial differential equations (PDE's) lead to (matrices of) integrals, and linear PDE's solutions may be expressed as a linear convolution filter (kernel or propagator)acting on the 'essential data ' (as in boundary element methods for example)

See also: Noether

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server
[BL] Philippe's name for a program (or part of a program) which displays menus to the user and accepts user input, then executes actions based on the user's menu choice. (Note that Philippe's "servers" are not the same as a server in a client-server architecture, as you might expect from the name.) An example of this kind of code can be found in the file moz.servers.lib0.f - see the subroutines with prefix "U1", as in "subroutine U1distributer".

SMP
[BL] (1) Shared Memory Processing in parallel computing: all processors have access to the same memory and thus may communicate with each other via the shared memory.
(2) Symmetric multiprocessor.

STRUCTURE CLASS, structure
[BL] Philippe's term for a collection of arrays and variables which, taken together, represent a particular kind of "object" in Mozart. (Note that Philippe's "objects" are not the same as the Object Oriented Programming (OOP) objects, since they do not have the features of the OOP objects.)

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template

[need a good definition here]

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WSSMP
Watson Symmetric Sparse Matrix Package. IBM's software to solve large sparse symmetric linear systems on either serial or parallel systems. See http://www.research.ibm.com/mathsci/ams/ams_WSSMP.htm

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