Database Design 1DL400. Assignment 2:2

Transcription

1 Uppsala Universit Department of Information Technolog Kjell Orsborn Assignment : - Database Design II Database Design DL00 Assignment : A Scientific Database for Mesh-Based Data. Goals This eercise consists of the development of a small scientific database application for storing and retrieving information about data for plane (D) discretizations (called a mesh or grid) of geometr domains. This mesh-based data can for eample be used to represent and present spatial data, such as temperature fields over a geometric objects. More specificall, ou should design and implement a small database for storing two tpes of mesh discretizations of geometr domains, as for eample used in finite element analsis applications. The student should implement schema definitions, populate the database and specif queries in Amosql, the quer language of sa.amos. The goal of this eercise is to give a practical eperience to develop a small database application using a functional and object-relational database management sstem (DBMS) that includes an object-relational quer language. The sa.amos DBMS b Stream Analze include the Amosql quer language that has similarities with the object-oriented etensions of the current SQL standard. The eercise include conceptual modeling using ER/EER modeling, transformation of the conceptual model into an object-oriented implementation data model and to implement the database b means of the sa.amos DBMS. Besides basic data, ou need to model and implement functionalit for quering the mesh database for geometric and phsical properties, such as coordinates and temperatures. This functionalit is tested through the list of sample queries listed in the instructions below and the quer response should be logged and reported in the results. The following steps should be performed: ER/EER modeling Transformation to a logical schema Implementation Defining and testing of quer eamples This eercise involves several open design and implementation choices to be decided upon and motivated b the student. This eercise is preferabl carried out in groups of two to three students.

2 . Preparations and background reading. The instructions to download and install sa.amos are provided on the assignments home page and we strongl recommend that ou familiarize ourself to sa.amos b running the included tutorials before ou start with the actual assignment. sa.amos can be used either in the computer labs at Uppsala Universit (Windows) or on our own laptop or desktop computer (Windows and Linu supported, and currentl through virtualization on Mac OS). There is also a short introductor seminar to this assignment, which is not mandator, but advisable to attend. It is advisable that ou design our solutions on paper before implementation. It can further be useful to stud the chapters on conceptual and logical data modeling and object databases treated in Chapters, and 0 in Elmasri and Navathe [EN0] or in Chapters, and in Padron-McCarth and Risch [PMR0]. Furthermore, material from lectures on object-oriented and object-relational databases sstems and quer languages. See also the assignment web page for additional information.. Instructions for the assignment The eercise consists of developing a scientific database application to handle information regarding scientific data for plane (D) discretizations (called a mesh or grid) of geometr domains. Your test data should include at least two different classes of meshes such as bi-linear quadrilateral and linear triangular meshes. Additional mesh classes can be selected individuall. A set of eample queries should also defined and tested. It is not intended that ou should design and implement the basic algorithm for performing the actual discretization. It is the information about factual meshes, such as topolog (structure) of the mesh and coordinate information that should be represented. A specific mesh can be built up b two kinds of basic elements, i.e. bi-linear quadrilateral or linear triangular elements, e.g., shown in Figure. In our case, a specific mesh is constrained to onl include one tpe of elements. The tpical structure of such meshes to be implemented are presented in the eamples in Figure and Figure. These kinds of discretizations can be viewed as an approimation of the geometr. Furthermore, other phsical quantaties can be approimated using the same tpe of interpolations. For instance, a scalar quantit such as the temperature T can be epressed as an interpolated temperature field for a bi-linear element as T = e e e e [ N N N N ] T T T T where N i e represent element shape functions that interpolates a field quantit inside the element using nodal point values for the field quantit (here nodal temperatures T i :s). The shape functions for the bi-linear element is given b

3 N e = ( ab ) ( ) N e = ab N e = ab ( )( ) ( )( ) N e = ab ( )( ) This interpolation can be used to represent data (using stored and derived data), for some temperature field of our choice. These representations can later be used to epress queries that retrieves field quantities over the geometr. For instance, what is the temperature for a specific coordinate. Observe that these epressions for the bi-linear element assume that element edges are parallell to the coordinate aes as illustrated in Figure. There are similar formulations for elements with more general forms as illustrated in Figure but that is outside of this assignment. At least the following concepts should be represented: mesh element node coordinate (- and -coordinates) element numbering node numbering (both local, i.e. per each element, and global, i.e. for a mesh) nodal temperatures (, ) (, ) b (, ) (, ) a Figure. Four-node rectangular element (bi-linear quadrilateral element)

4 n,(, ) n,(, ) e n,(, ) n,(, ) n,(, ) n,(, ) e n,(, ) Figure. Eample of plane -node bi-linear quadrilateral and -node linear triangular elements. Note that at least global node and element numbers should be able to be altered b a potential eternal application, e.g. for optimizing the topolog of the mesh. This ma influence the decision on how to choose kes. It should be possible to retrieve correct answers to the following queries:. What is the coordinate(s) of a specific node?. Which are the nodes of a specific element?. Which element(s) is a specific node part of?. Which nodes are shared b a set of two elements?. Which elements are adjacent to a specific element?. What is the size of the area of a specific element?. What is the size of the area for the complete geometr?. What is the opposite edge to a specific element edge (i.e. set of nodes)?. What is the complete surrounding edge of the geometr (i.e. a set of edges)? 0. What element is a specific coordinate inside of?. What temperature do we have at a specific coordinate (onl for the bilinear case)?

5 Other queries are welcome. At least two such additional queries should be defined. An additional and important assumptions or restrictions made b the student should be clearl motivated Figure. Test eamples for a mesh of bi-linear quadrilateral elements including information on global element and node numbers as well as node coordinates Figure. Test eamples for a mesh of linear triangular elements including information on global element and node numbers as well as node coordinates.

6 . Handing in Hand in an overview of the design, i.e. in an EER diagram, including eplanations to concepts and smbols, and source code for creating the database. Include solutions with sstem response to all the questions in the eercise as a printout of the interaction with sa.amos. This can be done b coping the results from the window where ou are running sa.amos to a tet file that ou print out and hand-in to our assistant. You do not have to hand in the answers to the eercises in the tutorial. Different design and implementation alternatives and choices, as well as problems or difficulties to perform certain parts of the eercise, should be clearl presented and motivated. References [EN0] Elmasri, R. and Navathe, S. B.: Fundamentals of Databases, th Edition, Addison-Wesle, 00, available e.g. at Akademibokhandeln. [PMR0] Padron-McCarth, T. and Risch, T.: Databasteknik, Studentlitteratur, 00, available e.g. at Akademibokhandeln.