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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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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
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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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
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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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
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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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 forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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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 forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
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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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 forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
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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Framework forDeveloping
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
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
Summary
Scientific application
development process
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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 forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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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 forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
Summary
Increment 1 -
Requirement Specification
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
Summary
Increment 1 -
Requirement Specification
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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Framework forDeveloping
ScientificApplications
Scientific
Applications and
SoftwareEngineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
Summary
Increment 1
Testing
CuTest systemCode assertionsfunction for testing the members of the array of xvalues in FBR
Increment 1 -
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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
Summary
System Design
Same as specified in Increment 1
Increment 2 -
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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
Summary
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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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
Summary
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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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
Summary
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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Framework forDeveloping
ScientificApplications
Scientific
Applications andSoftware
Engineering
Motivation and
Goals
Scientists’
development
practices
Framework forDeveloping
Scientific
Applications
Solving 1D and2D Schorödinger
Equations by
using DVR
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