framework for developing scientific applications: solving 1d and 2d schrodinger equation by using...

8/19/2019 Framework for Developing Scienti fic Applications: Solving 1D and 2D Schr odinger Equation by using Discrete Variable Representation Method

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Framework for

Developing

ScientificApplications

Scientific

Applications and

SoftwareEngineering

Motivation and

Goals

Scientists’

development

practices

Framework forDeveloping

Scientific

Applications

Solving 1D and2D Schorödinger

Equations by

using DVR

Summary

Framework for Developing Scientific

Applications: Solving 1D and 2D

Schrödinger Equation by using DiscreteVariable Representation Method

Bojana Koteska 1 Anastas Misev 1 Ljupčo Pejov 2

1Faculty of Computer Science and Engineering, UKIM, Skopje

2Faculty of Natural Science and Mathematics, UKIM, Skopje


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Framework for

Developing


Scientific

Applications and

SoftwareEngineering

Motivation and

Goals

Scientists’

development

practices


Scientific

Applications


Equations by

using DVR

Summary

Outline

1 Scientific Applications and Software Engineering

2 Motivation and Goals

3 Scientists’ development practices

4 Framework for Developing Scientific Applications

5 Solving 1D and 2D Schorödinger Equations by usingDVR

6 Summary


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Framework for

Developing


Scientific

Applications and

SoftwareEngineering

Motivation and

Goals

Scientists’

development

practices


Scientific

Applications


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using DVR

Summary

Scientific Applications

Scientific application

Software application that simulates activities from thereal world and turns objects into mathematical models

Designed to perform numerical simulations of natural phenomena in different scientific fields

Experiments with large amount of data, powerful

supercomputers, high performance computing andGrid computing

Developed by the scientists themselves and used inthe scientific research group


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Framework for

Developing


Scientific

Applications and

SoftwareEngineering

Motivation and

Goals

Scientists’

development

practices


Scientific

Applications


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Summary

Software engineering

Definition of SEAn application of a systematic, disciplined, quantifiableapproach to the development, operation andmaintenance of software, that is, the application of engineering to software


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Scientific

Applications and

SoftwareEngineering

Motivation and

Goals

Scientists’

development

practices


Scientific

Applications


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Summary

Scientific Application

Development

Differs from the development of commercialapplications, especially in the stage of testing

Software can not be tested based on users’requirements

Results compared to the results obtained from thereal experiments or based on theory

Additional changes in terms of planning,requirements elicitation, testing and developmentapproaches


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Scientific

Applications and

SoftwareEngineering

Motivation and

Goals

Scientists’

development

practices


Scientific

Applications


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using DVR

Summary

Motivation and Goals

Motivation

Survey among scientists - participants in the HighPerformance - South East Europe (HP-SEE) project

Goals

Change the current development practices

Development framework provides basis for a

complete scientific software development processSet of rules, recommendations and softwareengineering development practices

Application for solving 1D and 2D Schrödinger

equations by using the DVR


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Scientific

Applications and

SoftwareEngineering

Motivation and

Goals

Scientists’

development

practices


Scientific

Applications


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using DVR

Summary

Scientists’ development

practices

Learn programming independently or by otherscientists

Process of software development is only the processof coding

Get only scientifically correct results

Not interested in additional optimizations or

parallizationsIf a hypothesis is proven once, there is noneed for reprogramming that section


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Scientific

Applications and

SoftwareEngineering

Motivation and

Goals

Scientists’

development

practices


Scientific

Applications


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using DVR

Summary

Scientists’ development

practices

Lack of used software engineering formal methodsand practices

No requirements or any kind of documents

Requirements should only be discussed, but notwritten

Give importance to the quality of the algorithmrather than its realization

Test the implemented theory, not the algorithmimplementation

Test manually, do not use any testing tools


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Scientific

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Scientists’

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Scientific

Applications


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Summary

Framework for Developing

Scientific Applications

Incremental software development model

Changes in the process of evaluation, in test-drivendesign and short reports after each iteration

Fast delivery of increments and their evaluation

8 phases in each increment: planning,requirements definition, system design, testcases design, coding, testing, evaluation,writing short report


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Scientific

Applications and

SoftwareEngineering

Motivation and

Goals

Scientists’

development

practices


Scientific

Applications


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Summary

Scientific application

development process


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Scientific

Applications and

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Motivation and

Goals

Scientists’

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practices


Scientific

Applications


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Summary

Planning

Non-formal document which contains a list of

activities that should be performed in the nextiteration

What parts (modules) have to be coded in thatiteration

How they will be tested and evaluatedTasks should be assigned appropriately


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Scientific

Applications and

SoftwareEngineering

Motivation and

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Scientific

Applications


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Summary

Requirements Specification

Formally written requirements

Evidence of completed and future activities

Functional requirements and nonfunctionalrequirements

Fields:

IdName

Requirement typeVersionDescriptionHistory of changes


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Scientific

Applications and

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Motivation and

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Summary

System Design

Hardware and software systems requirements

Establish a system architecture

Examples: multicore processor, Grid,high-performance computing, libraries that provideparallel execution

Specification of compilers, integrated developmentenvironments (IDEs), platforms and operatingsystems


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Scientific

Applications and

SoftwareEngineering

Motivation and

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Scientists’

development

practices


Scientific

Applications


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Summary

Test Cases Design

Mostly related to functional requirementsUsing standardized formsBoundary values, source code analysisCode and branches coverage techniques

Fields:IdNameRequirement IdGoal

PreconditionsExecution environmentExpected resultsActual resultsTest case status (pass or fail)History of changes


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Scientific

Applications and

SoftwareEngineering

Motivation and

Goals

Scientists’

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Scientific

Applications


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Summary

Coding

Define more independent modules

Avoid declaration and definition of unused variablesRelease memory

Write comments

Optimizations and parallelization by using some

libraries (for example, OpenMPI, if the code iswritten in C).


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Motivation and

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Scientific

Applications


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Summary

Testing

White-box testing - tests designed to check thesource code

Non redundant test cases

Criteria that testing process is completed: all testsare performed successfully without errors, thecriteria for source code coverage and test models aresatisfied and validation by analytic solutions isachieved

Tests automation and tools

Frameworks for creating and running tests (C code:Check, CUnit, AceUnit, CuTest, etc.)

Integration testing


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SoftwareEngineering

Motivation and

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Scientific

Applications


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Summary

Evaluation

Evaluated only by a limited number of users

Accuracy of results is based on theory and

experiments

Developing experience and learning techniques forguessing or past errors can help

Found errors should be sorted by priority

Critical errors should be marked as errors withhigher priority


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SoftwareEngineering

Motivation and

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Scientists’

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Scientific

Applications


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Summary

Writing Short Report

Document that describes the finished tasks in thecurrent iteration

Important when a new member joins the team

Can help to further improving and upgrading theapplication


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Scientific

Applications and

SoftwareEngineering

Motivation and

Goals

Scientists’

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practices


Scientific

Applications


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Summary

Scientific Problem

DVR’s - representation whose basis functions are

localized about discrete values of the variablesDVR’s provide efficient numerical solutions toquantum dynamical problems

Schrödinger equation - partial differential equation

that describes the dynamics of system at atomic andmolecular level


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Scientific

Applications and

SoftwareEngineering

Motivation and

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Scientists’

development

practices


Scientific

Applications


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Summary

Scientific Problem

Time independent Schrödinger equation

H ∗ Ψ = E ∗ Ψ (1)

where H is the Hamiltionian operator, Ψ is the wave

function of the quantum system and E is the energy of the state Ψ

Time dependent Schrödinger equation

i ∗ ∂ Ψ

∂ t = H ∗ Ψ (2)

where H is the Hamiltionian operator, Ψ is the wavefunction of the quantum system, is the PlanckConstant divided by 2Π and ∂

∂ t is a partial derivative with

respect to time t


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Scientific

Applications and

SoftwareEngineering

Motivation and

Goals

Scientists’

development

practices


Scientific

Applications


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Summary

Increment 1 - Planning

define the inputs and outputs of the module forsolving 1D and 2D Schrödinger equation

define developing environment, software andhardware

split the algorithm in modules

define inputs and outputs for each module

create tests for modules by choosing any tool for

test automationdevelop all submodules needed for the module forsolving 1D and 2D Schrödinger equation

perform tests and evaluate the results

correct errors if any

Increment 1


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Scientific

Applications and

SoftwareEngineering

Motivation and

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Scientists’

development

practices


Scientific

Applications


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Summary

Increment 1 -

Requirement Specification

Functional requirements:

Module for multiplication of two 2D arrays

Module for making a diagonal 2D array

Module for multiplication of a scalar and a 2D array

Module for making an identity 2D array

Module for addition of two 2D arraysModule for making a transposed 2D array

Increment 1


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Motivation and

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Scientific

Applications


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Summary

Increment 1 -


Functional requirements:

Structure for a file row which contains three doublenumbers.

Structure for a file which contains array of elementsof type ”structure for a file row” and number of rows of the file (integer).

Module for reading data from file

Module for sorting rows in file

Module for calculating eigenvalues

Module thcheby for calculating array of x-values,y-values(2D), transformation matrices for x and yvalues in finite basis representation (FBR)

Increment 1


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Scientific

Applications and

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Motivation and

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Scientists’

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practices


Scientific

Applications


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Summary

Increment 1 -


Nonfunctional requirements:

Algorithm for array sorting should have complexity

smaller then O (n2).Application should be scalable (for example, wheninput data size increases, dynamic memoryallocation must be used).

Memory used by the objects should be releasedwhen they are not used anymore.

Increment 1 -


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Scientific

Applications and

SoftwareEngineering

Motivation and

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Scientists’

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Scientific

Applications


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Summary

Increment 1 -

System Design

Single processor machine

C compilerCode editor

Any operating system

Results provided to the standard output

CuTest framework for testing

Increment 1 -


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Scientific

Applications andSoftware

Engineering

Motivation and

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Scientists’

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Scientific

Applications


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Summary

Increment 1

Test Cases Design

Test case for (thcheby module)

deltax is the difference between themaximum(xmax) and minumum value of x(xmin);

deltay is the difference between themaximum(ymax) and minumum value of y(ymin);

nx1 is the number of x points increased by 1;

nxy is the number of y points increased by 1;

The i -th member of the array of x values (ptsx) hasthe value ((i + 1) ∗ deltax ∗ 1.0)/nx 1 + xmin

The i -th member of the array of y values (ptsy) hasthe value ((i + 1) ∗ deltay ∗ 1.0)/ny 1 + ymin

Increment 1 -


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Motivation and

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Scientific

Applications


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Summary

Increment 1

Test Cases Design

Test case for (thcheby module)The i -th member of the array of x values in FBR(fbrtx) has the value (((i + 1) ∗ Π)/deltax )2;

The i -th member of the array of y values in FBR

(fbrty) has the value (((i + 1) ∗ Π)/deltay )2;The element at the position (i , j ) of thetransformation matrix for x values (Tx) has thefollowing value

2.0/nx 1 ∗ sin((i + 1) ∗ ( j + 1) ∗ Π/nx 1)The element at the position (i , j ) of thetransformation matrix for y values (Ty) has thefollowing value

2.0/ny 1 ∗ sin((i + 1) ∗ ( j + 1) ∗ Π/ny 1)

Increment 1 -


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Motivation and

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Scientists’

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Scientific

Applications


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Summary

Increment 1

Coding

Code is organized in modules

Coding performed after the specification of the testcases

Arrays defined by using pointersMemory released always when possible

Calculation of eigenvalues performed by using theGSL library

Sorting implemented by using the quick sort methodComments for describing the modules, variables,cycles and statements

Concise naming of the variables and methods

Increment 1 -


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Motivation and

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Summary

Increment 1

Testing

CuTest systemCode assertionsfunction for testing the members of the array of xvalues in FBR

Increment 1 -


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Motivation and

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Scientific

Applications


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Summary

Increment 1

Evaluation

Comparing the results from our application to

results from the provided code in Mathematica bythe Upssala University

Test the convergence of the results with increasingthe density of grid points

Several errors in the modules were found and theywere corrected

Increment 1 -


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Summary

Writing Short Report

All modules specified in the requirements section

were written and testedErrors were corrected and all tests passedsuccessfully

All nonfunctional requirements were taken into

consideration

I 2 Pl i


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Scientific

Applications


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Summary

Increment 2 - Planning

Adapt the input for 1D and 2D equation

Integrate all modules into one module for solving 1Dand 2D Schrödinger equation

Create tests for the module for solving 1D and 2DSchrödinger equation

Perform tests and evaluate the results

Correct errors, if any

Increment 2 -


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Scientific

Applications


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Summary

Functional Requirements

Functional Requirements:

Module for making the interpolation function (PES)and energy list (pel)

Module for calculating 1D and 2D Schrödingerequation

Increment 2 -


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System Design

Same as specified in Increment 1

Increment 2 -


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Test Cases Design

Two test cases

The conditions included in the test case for the firstmodule in this increment are for interpolationfunction

The second test case only checks the output results

Important thing here is the proper modulesintegration

Increment 2 -


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Coding

The module for calculating the 2D Schrödingerequation was developed

This module is appropriate for solving 1DSchrödinger equation by eliminating the calculationswhich include the second coordinate y

The most convincing part here was programming of the interpolation method

Increment 2- Testing and


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Evaluation and Short Report

Two tests created with CuTest framework

Results were compared to the results from theprogram in Mathematica

An algorithm for Hermite interpolation wasprogrammed

Summary


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Summary

Summary

Framework for developing scientific applications - allphases of the development process

Application for calculating 1D and 2D Schrödingerequation

Understandable code organized in modules,documentation and generated tests

Test the framework on large scientific applicationsCheck if this development process can be applied todifferent scientific applications

framework for developing scientific applications: solving 1d and 2d schrodinger equation by using...

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