A Guide for Proposal Writing Call for Proposals of ...

A Guide for Proposal Writing/ FY2020 Ver.1.0 (2019/08/22)

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A Guide for Proposal Writing Call for Proposals of projects using the HPCI System

in Fiscal Year 2020

This document states how to fill out application forms (Additional sheet 1&2) for research projects using the HPCI System. Please follow the instructions below when preparing the application documents. Note for applicants: The following procedures are necessary for application.

Please note the following points when you prepare/submit the documents. a. Preparation of Application Form (Additional Sheet 1)

Please make sure - To clarify that your proposal agrees with 2 (3) “Conditions of Use” - To use the latest version of the form - To give the document 15 pages at maximum - To upload it in PDF format

b. Preparation of Program Information Sheet (Additional Sheet 2) Please make sure - To give descriptions for each program (with referring to the guideline below) - To use the latest version of the sheet - To upload it in Excel format Note that the submission of the Program Information sheet (Additional Sheet 2) is not necessary if requesting the ABCI system from AIST.

c. Submission to Online Application System - After completion of data input to the system, please print out Web Application Form by pushing “Print” button. Then please send the form to the address below via postal mail, with signature of the Project Representative, the name of the organization to which the Project Representative belongs, and the representative’s name of the organization with his/her signature. Attachment of a. or b. is not necessary.

d. Consistency of Proposal Documents - Please make sure that all the information including requesting resources, program name(s), and project members is consistent among the application form (Additional Sheet 1), the program information sheet (Additional Sheet 2), and the online application.

Please consult Helpdesk bellow if you have any questions.

E-mail : [email protected] Phone: +81-78-940-5795

a. Preparation of Application Form (Additional Sheet 1) [PDF] b. Preparation of Program Information Sheet (Additional Sheet 2) [Excel] c. Submission to Online Application System

A Guide for Proposal Writing/ FY2020 Ver.1.0 (2019/08/22) FY2020 Application Form Ver.1.0 (2019/08/22)

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Note) This is the guideline to fill out the application form (Additional Sheet 1). Please download and use the

actual application form.

1 Significance of the Research 1.1 Purpose of the Research

Provide an overview briefly in the beginning. Then, describe the whole idea of the research and the specific

purpose with citing literatures if any. Particularly, the following points must be described clearly and

specifically.

1) Scientific background for the research (e.g., domestic and overseas trends and the positioning of the

research; how the applicant has reached the concept based on their achievements in earlier research

works; and if the applicant intends to develop the past research achievements, describe the contents.)

2) What will be elucidated and to what extent will it be pursued during the research period?

3) Characteristics and originality of the research in the area.

In this section 1. 1, indicate that your proposal covers the following points by underlining places applicable. * Junior Researcher Promotion Projects

The proposed project has excellent ideas which promise further development of the research in the future.

* Industrial Use Projects (Non-proprietary)

The proposed project is an industrial project to demonstrate the effectiveness and usefulness of the highly

parallel simulation technology.

1.2 Expected Achievements and Ripple Effects * If your proposal is for “Junior Researcher Promotion Projects”, indicate that its accomplishment will lead to

further development of the research in the future.

* State it if you have any definite schedules to publish achievements (e.g. in peer-reviewed papers, electronic

journals, published technical report of companies, presentations in conferences, patent application, etc.).

* If you intend to make the second or third choice, “Expected Achievements and Ripple Effects” needs to be

described for each choice.

[First choice] Resource Provider Name/ Computational Resource Name:

[Second choice] Resource Provider Name/ Computational Resource Name:

[Third choice] Resource Provider Name/ Computational Resource Name:

Project Name

Project Representative

Affiliation：

Name:


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2 Research Plan and Method * If the difference in characteristics of the first, second, and third choices induces any changes for the Research Plan and Method, it also needs to be described.

2.1 Research Plan and Method Provide an overview briefly in the beginning. Then, describe the details of the research plan and the methods

for achieving the objectives clearly and specifically with citing literatures if any. The plan should be considered

from different angles, such as an action to take in the event the research does not progress as originally

planned.

In addition, for each application program to be used, describe the reason for selecting the program, the

calculation methods (calculation model, analysis method, parallelization techniques, etc.), the applied

verification methods from a viewpoint of V&V (Verification and Validation), etc.

2.2 Utilization Plan of Computational Resources 2.2.1 Requesting Computational Resources (for each system) (1) Summary of Requesting Resources

* The first-choice system must be consistent with the system written in the Online Application System. If

inconsistency is found, the input entered in the Online Application System will be adopted with

precedence.

* The second or third choice cannot be specified in the Online Application System. Please request them in

this form if any.

[First choice] *Describe the same information as the Online Application System Provider Name/

Computational Resource Name

[Shared/Dedicated] Class Name Available period Amount of resources to request

A Center, B University/ X system

[Shared use] Classification none

2020/04/01-2021/03/31

240,000 NH

Local Storage 5,400 GB

If requesting multiple computational resources (for pre/post processing etc.)

Local Storage

* Please refer to the list of “HPCI Resources and Application Information in FY 2020” for the Computer Name,

Available Period, and Amount of Resources to request. Make sure to fill in the information per class unit

(whole year, half-year, or quarter).

[HPCI Resources and Application Information in FY 2020]

http://www.hpci-office.jp/materials/r02_boshu_hpci_resource_e.pdf

* Add a new row to the table if needed.


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[Second choice] *The second choice cannot be specified if requesting the concurrent use of multiple computational

resources. Provider Name/

Computational Resource Name [Shared/Dedicated]

Class Name Available

period Amount of resources to request

C Center, D University/ Y system

[Shared use] Classification none

2020/04/01～2021/03/31

236,110 NH

Local Storage 6,000GB

* Add a new row to the table if needed.

(2) Utilization plan

* Describe a specific utilization plan in accordance with the research plan. Make sure to show reasonable

grounds for the estimated amount of resources requesting. If you use multiple programs, clearly indicate the

program for which the utilization plan is.

* Make sure that the maximum number of nodes and the corresponding data size that you describe here do

not conflict with the “Target value of #Nodes” and the size of “Input data for target” in the program

information (Additional Sheet 2).

< Example >

[First choice]

・ Project Period: April 2020 - March 2021 ・ Requesting Resources: A Center, B University/ X system ・ Program

Program

name Input data set name

Data size

(#grid points) #time steps

Execution

confirmed

PPP Input Data A (low resolution) 2,000,000 400 Yes

PPP Input Data B (medium resolution) 16,000,000 1,000 No

PPP Input Data C (high resolution) 128,000,000 10,000 No

(Utilization plan for the first half-year) 1. Carry out preliminary calculations of the model a and b with the low-resolution data set, and investigate ideal

parameters for the medium-resolution calculations: April

8 nodes x 300 sec. x 10 times = 7 node-hours per model

Model a, b: 7 node-hours x 2 models = 14 node-hours

2. Carry out calculations of the model a, b using the medium-resolution data: May

16 nodes x 3,000 sec. x 20 times = 267 node-hours per model

Model a, b: 267 node-hours x 2 models = 534 node-hours

3. Carry out calculations with the high-resolution data and evaluate the result (1): June - September

Carry out calculations of model a and b:

256 nodes x 20,000 sec. x 40 times = 56,889 node-hours

Model a and b: 56,889 node-hours x 2 models = 113,778 node-hours


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(Utilization plan for the last half-year) 4. Carry out calculations with the high-resolution data and evaluate the result (2): October - March

256 nodes x 20,000 sec. x 40 times = 56,889 node-hours per model

Model a, b: 56,889 node-hours x 2 models = 113,778 node-hours

====================================================================

<Requesting Amount of Resources>

April 2020 : 14 node-hours

May 2020 : 534 node-hours

June 2020 - September 2020 : 113,778 node-hours

October 2020 - March 2021 : 113,778 node-hours

Total (April 2020 - March 2021) : 228,104 node-hours

(Requesting resources with system unit considered : 240,000 node-hours)

====================================================================

* Total amount resources should be stated per requesting system.

(Annual plan for the use of local storage)

Local storage is needed to store the following data during the project period.

- 1 GB is needed for one case of the low-resolution data: 1 GB x 10 cases x 2 models = 20 GB

- 2 GB is needed for one case of the medium-resolution data: 2 GB x 20 cases x 2 models = 80 GB

- 30 GB is needed for one case of the high-resolution data (1): 30 GB x 40 cases x 2 models = 2,400 GB


- 500 GB is needed temporarily

Total : 5,400 GB

(Requesting space with system unit considered : 5,400 GB)


[Second choice]

・ Project Period: April 2020 - March 2021 ・ Requesting Resources: C Center, D University/ Y system ・ Program: Same as the first choice

(Utilization plan for the first half-year) Same as the first choice

(Utilization plan for the last half-year) Same as the first choice


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==================================================================== <Requesting Amount of Resources>

April 2020 : 14 node-hours

May 2020 : 534 node-hours

June 2020 - September 2020 : 113,778 node-hours

October 2020 - March 2021 : 113,778 node-hours

Total (April 2020 - March 2021) : 228,104 node-hours

(Requesting resources with system unit considered: 236,110 node-hours)

====================================================================


(Annual plan for the use of local storage)

Local storage is needed to store the following data during the project period.

- 1 GB is needed for one case of the low-resolution data: 1 GB x 10 cases x 2 models = 20 GB

- 2 GB is needed for one case of the medium-resolution data: 2 GB x 20 cases x 2 models = 80 GB



- 500 GB is needed temporarily

Total : 5,400 GB

(Requesting space with system unit considered : 6,000 GB)

2.2.2 Class Setting (if HPCI shared computational resources are requested) For the HPCI resources, proposals are classified into two and screened in the respective classes: The L class for

projects needing larger resources and the S class for projects needing smaller resources. If you request HPCI

resources, see Appendix 1 “Classification of the application of the HPCI System” and Appendix 2 “HPCI shared

computational resources and HPCI Shared Storage in FY 2020” in the “Proposal Preparation Instructions”, and state

in which class your request is classified.

Class (Select L class or S class)

2.2.3 HPCI Shared Storage (Fill out only if you request it.) * If HPCI Shared Storage is needed, write down the requesting amount of resources (GB) and a basis of the estimate. * If you request “CPU Simultaneous Use”, state that your project has a plan to use the storage system together with the HPCI System, carry out data analysis before the use as planned, the data on the HPCI Shared Storage are moved and stored in the storage facility of the user before the completion of the project. HPCI Shared Storage： GB

Basis of the estimate:


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2.2.4 Data Management Plan Describe the policy regarding the storage of research data and disclosure/non-disclosure of the data. If you plan to disclose the research data and promote the utilization by providing them to a third party, describe the way and structure to provide the data, how it is expected to be used, and how you plan to promote the use in public.

2.3 Preparation Status of the Application Program Application program name: (state the name of the application program) Describe preparation status of the program for carrying out your project. For each program, the following points

should be stated.

1) The development of the program has finished, and the operation has been tested (no matter on what system(s)

or with what data).

2) The program has been tested on the requesting system(s) (no matter with what data)

3) The program has been tested on the requesting system(s) with a similar type of calculation and the same data

size.

4) The estimated parallel efficiency for the target number of nodes is sufficient in carrying out the project (50% or

higher is expected).

The target number of nodes for the production run:

Estimated parallel efficiency: %

* The same numbers should be specified as the “target value of #Nodes” (*10(1)) and the “estimated parallel

efficiency” (*16) in the program information sheet (Additional Sheet 2).

* If there is a prospect that enough parallel efficiency will be obtained such as by scale-up of the data, describe it,

too.

* If there is no prospect of such performance improvement at present and estimated parallel efficiency is not

sufficient, include the performance improvement measures in the research plan, or lower the target value of

nodes for production run.

2.4 Necessity of the Requesting Computational Resources Describe the necessity of the requesting computational resources in association with the

research plan.

*[1] If requesting HPCI computational resources, describe that your research project challenges for large-scale

and large capacity computing, or is promising to continue to the post-K computer in the future.


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*[2] If requesting the concurrent use of multiple HPCI computational resources, in addition to *[1], describe

why all systems are needed. (For example, in the case of using mainly one system and using another system for

pre/post processing, or the case that the requesting system will stop during the project’s period due to the

system update, so it should continue to use the successor system).

*If you specify the second or third choice, in addition to [1], describe the basis that you realize the research plan

with computational resources of the second choice.

2.5 Organizational Plan for the Project Execution, and Staffing Plan If the research plan is being implemented by multiple organizations, describe the specific role of each organization

in the research team (using figures, tables, and other visual aids). For each project member, describe the following

points: the name of the organization to which the member belongs, their realm of expertise, whether or not to use

the computing resources, their role(s), and their achievements, etc.

In the staffing plan, describe if there is a plan to hold a training session for project participants with no history of

using the requesting computational resources. Also, the plan should also include possibilities of member change

during the project period.

State it if your project intends to add new members to the team and provide on-the-job trainings (OJT) in the view

of developing human resources.

* If you apply for the consortium type of an Industrial Use Project (Non-proprietary), state

- that your project consists of a consortium or group of five or more companies;

- that there are ongoing or scheduled activities;

- that clarification of role sharing among participating companies.

* Accounts of computational resources are issued for the members who are listed on the Online Application

System. Except for members who will be added during the project period, make sure that the input on the Online

Application System is consistent with the persons for whom "use" is written in the "Whether to use the resource"

field of the Table below.

* In principle, all the project members must be listed in the application form. If it is not possible to list names, the

reason needs to be stated in the form. (e.g. a new member is expected to be assigned but his/her name is unknown,

some tasks are planned to be outsourced to a vendor of application software, etc.)

< Example >

(Organization Chart) Organization Roles

I University To carry out the project taking a principal position

L Research Institute Develop calculation models

J Company Support: Faster tuning of the program

K University Cooperation: Advice from scientific viewpoints

(The above chart can be replaced by a diagram showing an organization structure.)


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(Project Members)

Project Member Affiliation Expertise Whether to

use the resource

Roles

Researcher A I University Numerical fluid dynamics, turbulent flow

use Project Representative, Verification of results, Analysis

Researcher B L Research Institute

Mechanical engineering use

Deputy Project Representative, development of computational models, problem definition, preparation of input data

Researcher C I University Numerical fluid dynamics, turbulent flow

use Contact Person, program porting, production run,

External Supporting staff D J Company High performance

computing use Tuning of the program

Collaborator E K University Turbulent flow no use Advice from scientific viewpoints

(Experience and Achievements) Researcher A has experiences in the field of computational fluid dynamics … Researcher B … Researcher C has five-years of experience in program porting … (Staffing plan & training) April: B and C will take “User seminar” April: External support staff D will be contracted. Addition of the project member will be requested. May: D will take “User seminar”.

3. Research Information Relevant to This Proposal 3.1 Ongoing Projects

- Ongoing project ID:

- Ongoing project name:

- Status of the ongoing project (goal achievement status etc.)

* If there is a project that is currently ongoing as an HPCI research project, indicate the "Project ID" and

"Project Name", and also describe the status of achievement toward the goal of the project, unresolved

issues and possibilities of development in the present project, etc.

3.2 Related Projects Research project using the HPCI Systems If your project is not a continuous project but related to any project using the HPCI System, state the

information about the project below (e.g. the status of a K General Trial Use project carried out prior to this

proposal).

- Project ID

- Project Name:

- Status of the related project (goal achievement status etc.)


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Research plan for collaborating with Large Experimental Facility projects. If your project is collaborating with Large Experimental Facility projects*, state the information of the

collaborative project (including “Collaborating Facility Name”, “project No.”, “project Name”, “period of use”,

etc.).

- Collaborating Facility Name

- Project ID

- Project Name

- Outline

* The collaboration with Large Experimental Facility projects is expected to lead to excellent results by

complementarily enhancing the effectiveness of the experimental approach with numerical simulations.

Other related research If there are any other related researches using parallel computational resources, describe the achievements

and research results briefly.

4. Research Achievements References Out of the research papers/articles, books, industrial property rights, conference presentation, news release, and

other outputs that project members have presented, select the important publications related to this research

project, list them in the sequence from new to old with serial numbers assigned.

1) For published research papers/articles, state the title, the names of authors, name of the journal, referee

reading (or not), volume, page numbers of the initial and final pages and the year of publication.

2) The above-mentioned sequence of such items is not compulsory as long as all of the items are included. If

there are many authors, only state several authors (if any authors’ names are omitted, state the number of the

authors and the order on the author list for the related researchers). The Project Representative should be

marked with a double underline, and the project member with a single underline.

[1] I. Kei, J. Kobe, M. Minatojima, ”A numerical method for ～”, International Journal for Numerical Methods ～, Vol.

78, pp.123-145, (2015). (peer-reviewed)

[2] News release：”World’s First Successful turbulence simulation of ...”, (2015).

[3] I. Kei, J. Kobe, ”Turbulence analysis of ...”, **th ~ Fluid Symposium, Oral presentation, (2014).

[4] I. Kei, J. Kobe, “Computational Analysis...”, Proceedings of ～, (2013). (peer-reviewed)

5. Validity to Perform the Project * State that the execution of the project and utilization of the results will be limited to peaceful purposes and

proper in terms of Basic Act on Science and Technology and social values.


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Eligibility of Junior Researcher Promotion Project Applicants To apply for the junior researcher promotion project, all the members must be less than or equal to 39 years of age at the time of April 1, 2020 (born on or after April 2, 1980). Only if you want to apply to it, please fill in the age of the project members.

Name Age (as of April, 2020)

AAA BBBB xx years old

CCC DDDD xx years old

EEE FFFF xx years old


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Guide for Writing Program Information (Additional Sheet 2) Ver.3.5 1. Program Information (Additional sheet 2) is an Excel sheet. 2. Fill out one sheet per program that you will run in the research project. 3. To calculate the parallel efficiency, measure with two cases. For the scaling method, select either

Strong Scaling or Weak Scaling. * Strong scaling... the elapsed time for fixed problem size as number of processing units are increased

Weak scaling...the elapsed time for fixed computational work per processing unit as problem size is increased

4. To blue cells, fill in data directly. To yellow cells, select a corresponding item from the pull-down list. To green cells, select a corresponding item from the pull-down list or fill in data directly. Light orange cells are automatically calculated in accordance with your prior inputs.

5. In the cell of actual measurement information, describe the measured performance by using the same kind of input data* for your planned production run. Performance information measured in the past can be used. * the same kind of input data...the data used to perform the same routine or function in the program.


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Measuring method

(A) Strong Scaling (this would be the case for most of the applicants)

- Strong Scaling is the way to measure the program performance by checking how fast the program runs with fixed

problem as processing units are increased.

* Provide the data at two measurement points (green and red in

the figure), and the target degree of parallelism (number of

processors, CPUs, or cores that you plan to execute on the

system; the purple point in the figure).

* The green point should be the max. parallel number that you

measured at the execution machine you used for performance

measurement.

* The red point should be the data with less parallelism (less

than half) than green.

Note for Strong Scaling (see the example of the sheet below.)

• Use the same size of input data for two measurement points (shown in green and red triangles below.)

• The degree of parallelism is calculated by the sheet if you enter the number of nodes, processors, and threads.

Select Strong scaling


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(B) Weak Scaling (see the example of the sheet below.)

- Weak Scaling is the way to measure program performance by checking how fast the program runs with increasing

processing units and assigning the fixed computational work to each unit.

* Provide the data at two measurement points (green and red in

the figure), and the target degree of parallelism (number of

processors, CPUs, or cores that you plan to execute on the

system; the purple point in the figure).

* The green point should be the elapsed time measured with the

max. processing units on the execution machine.

*The red point should be the elapsed time measured with a

lower number of processing units (a lower multiple of the green

point) and with the same computational work per unit.

Note for Weak Scaling

• For the second measurement input data (see green triangle), use the data size twice as large as the first (see

red triangle).

• The degree of parallelism is calculated by the sheet if you enter the number of nodes, processors, and threads.

Select Weak Scaling


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******************************************************* Description of input items (Red characters is required input) ******************************************************* *1 Name of execution machine

Fill in the name of the system used for performance measurements. If one of the HPCI computational resources was used, choose it from the pull-down list or input it. *2 Parallelization method

If you use MPI, OpenMP, or Automatic parallelization to parallelize your program, select “use”. If not, select “no use”. If another parallelization method is used, indicate the name of the method. *3 Measuring method

Select either Strong scaling or Weak scaling as the measuring method. *4 Information of allocation

Fill in (1) with the number of nodes, (2) with the number of MPI processes in each node, and (3) with the number of multi-threads in each MPI process that you are using for your current simulation. In the case of Flat MPI, fill in 1 to (3) #Threads/Process. *5 Input data when measured (type and size)

Enter the type and size of input data. The type should be indicated by a subject of your simulation; for example, names of materials, structures, globe or regions around Japan. The size can be indicated by the numbers of data such as grids, elements or atoms. Specify the same type of input data for your planned production run.

If the size of input data per process is adjusted to be similar to the size of input data for your planned production run per process, accuracy of the performance estimation will be improved. *6 Execution time

Fill in the cell with execution time (elapsed time) of two cases, parallelization degree m and n (>=2m), in seconds. *7 Effective performance

If the floating point operation is a major part of the computational processes, enter Giga Floating Point Operations Per Second (GFLOPS) and obtain the effective performance by dividing the measured floating point operations per second (FLOPS) by the theoretical peak FLOPS of the system if possible. These values should be based on the total execution, not on the specific subroutines of the program.

If the floating point operations are not major part of computations, enter the million instructions per second (MIPS) or million operations per second (MOPS) instead of both FLOPS and effective performance. Other units of performance indicators can be chosen in accordance with the type of program execution in answering to this question. If proper measurement tools are not available, you can skip these cells.


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*8 Usage computational resource Select the name of HPCI computational resources which you are planning to use from the pull-down

list. *9 Input data for target (type and size)

Enter the type and size of input data for your program to run on your requesting system. *10 Information of allocation for target

Fill in (1) with the number of nodes, (2) with the number of processes in each node, and (3) with the number of threads in each process that are needed for your target simulation. ****************************************************************************** From here all values will be automatically calculated in accordance with your input. ****************************************************************************** *11 Degree of parallelism

The degree of parallelism will be automatically calculated as the product of the values of three variables; (1), (2), and (3) as shown in *4. *12 Effective parallelization ratio α (%)

The effective parallelization ratio is calculated differently depending on the case of strong or weak scaling. The effective parallelization ratio of both strong scaling and weak scaling are calculated automatically in this Excel sheet based on the different formulae. Utilize these values to set the target of the project (cf. *16 Target degree of parallelism). The details of the equations are as follows;

(a) In case of strong scaling

The ratio of the elapsed time of the parallelized part to the total elapsed time and that of the serial part to the total are defined as α and (1-α), respectively. This α will be deduced by employing the Amdahl’s law. With this evaluation method, the effective parallelization ratio including the overheads due to parallelization can be obtained. Specifically, the effective parallelization ratio can be obtained through the following calculations.

Measure elapsed times, Tm and Tn at two points of parallelism, m and n (n>=2m). Here, we define T1 as

an elapsed time with the parallelism of 1. Following Amdahl's law, the ratio of speed-up with the

parallelism of m and n can be defined as:


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𝑆𝑆𝑛𝑛 =𝑇𝑇1𝑇𝑇𝑛𝑛

=1

1 − 𝛼𝛼 + 𝛼𝛼𝑛𝑛

(1)

𝑆𝑆𝑚𝑚 =𝑇𝑇1𝑇𝑇𝑚𝑚

=1

1 − 𝛼𝛼 + 𝛼𝛼𝑚𝑚

(2)

By eliminating T1 from equations (1) and (2), the effective parallelization ratio of strong scaling αs is expressed as:

𝛼𝛼𝑆𝑆 ≡ α =𝑇𝑇𝑚𝑚 − 𝑇𝑇𝑛𝑛

�1 − 1𝑛𝑛� 𝑇𝑇𝑚𝑚 − �1 − 1

𝑚𝑚�𝑇𝑇𝑛𝑛 (3)

If you enter values of Tm and Tn in the Excel Sheet for the case of strong scaling, αs will be calculated

automatically by using the equation (3) and shown in terms of %. The calculated effective parallelization ratio might be larger than 1 (unity) or negative, if the elapsed

time is measured with small m. Choose proper conditions to avoid such situations.

(b) In case of weak scaling The elapsed time of the parallelized part is assumed to be constant. In addition, some part of the serial

part is also assumed to be constant. The elapsed time of these parts is assumed to be α in total, and the residual serial part whose elapsed time is dependent on the size of data is assumed to increase in proportion to the size of data. From these assumptions, the relation below holds:

𝑇𝑇𝑛𝑛 ∶ 𝑇𝑇𝑚𝑚 = 𝛼𝛼 + (1 − 𝛼𝛼)𝑛𝑛 ∶ 𝛼𝛼 + (1 − 𝛼𝛼)𝑚𝑚 (4) The effective parallelization ratio of weak scaling αw can be solved as follows:

α𝑊𝑊 ≡ 𝛼𝛼 =𝑛𝑛𝑇𝑇𝑚𝑚 −𝑚𝑚𝑇𝑇𝑛𝑛

(1 −𝑚𝑚)𝑇𝑇𝑛𝑛 − (1 − 𝑛𝑛)𝑇𝑇𝑚𝑚 (5)

In case of weak scaling measurements of Tm and Tn, αw will be automatically calculated with the

equation (5).

*13 Parallel Efficiency (En) The parallel efficiency ‘En’ for a given degree of parallelism ‘n’ indicates how much the program is

efficiently accelerated by parallel processing. ‘En’ is given by the following formulae. Although their derivation processes are different depending on strong and weak scaling, derived formulae are the same.

(a) In case of strong scaling In case of strong scaling, ‘EnS’ is calculated automatically with the following formula, and is displayed in

percentage in the sheet:


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𝐸𝐸𝑛𝑛𝑆𝑆 =𝑆𝑆𝑛𝑛𝑛𝑛

=1

(1 − 𝛼𝛼𝑆𝑆)𝑛𝑛 + 𝛼𝛼𝑆𝑆 (6)

where α is the effective parallelization ratio, given by the formula (3) with the speed-up ratio ‘Sn’, given by Amdahl’s law. For example, if n=100, and ‘Sn’ = 20, 50, and 100 times, ‘EnS’ are 20, 50, and 100%, respectively. If α exceeds 1, ‘EnS’ becomes larger than 100% or less than 0%, and as a result, Amdahl’s law is no longer applicable. Then, please try to avoid those situations by properly choosing conditions of performance measurement.

(b) In case of weak scaling In case of weak scaling, the amount of computation for a given degree of parallelism ‘n’ is n times larger

than the case with n=1. Ideally, the elapsed time should be the same regardless of whether the software is running in serial or parallel processing. In this case, ‘EnW’ is supposed to be 100%. ‘EnW’ is 50% if the elapsed time in parallel processing is twice as long as that of the serial processing, and 20% if 5 times. Such ‘EnW’ is expressed as a simple ratio of the elapsed time in serial processing to that in parallel processing, and is calculated with a simple formula as follows:

𝐸𝐸𝑛𝑛𝑊𝑊 =𝑇𝑇1𝑇𝑇𝑛𝑛

=1

(1 − 𝛼𝛼𝑊𝑊)𝑛𝑛 + 𝛼𝛼𝑊𝑊 (7)

Here, (7) is derived from (4).

Although the ways to derive the effective parallelization ratio α are different depending on strong and weak scaling cases, the formulation of the ‘En’ is the same in the end in both cases. ‘EnW’ is calculated automatically with the formula (6) or (7), and is displayed in percentage. *14 Guideline for degree of parallelism

The degree of parallelism ‘n’ which gives ‘En’ = 50% is calculated automatically with the following formula (9).

𝐸𝐸𝑛𝑛 =1

(1 − 𝛼𝛼)𝑛𝑛 + 𝛼𝛼=

12

(8)

n =2 − 𝛼𝛼1 − 𝛼𝛼

(9)

This value is just a guideline. You can set a larger degree of parallelism as a target, especially if you are

planning to speed up your program after starting your project, or if the reduction of the elapsed time is more important than improvement of the parallel efficiency.


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*15 Target degree of parallelism

The target degree of parallelism will be automatically calculated as the product of the values of three variables; (1), (2), and (3) as shown in *10 *16 Estimated parallel efficiency (Ex)

The estimated parallel efficiency (Ex) is calculated automatically with the formula (6) or (7) by assigning the target degree of parallelism (x) to ‘n’, and the result is shown in %. Use this value to check whether the value of (x) is appropriate or not.

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