代做PHYS 52015、代写C/C++设计程序

日期：2024-01-03 09:57

Coursework: High-Performance Computing

Module: Introduction to HPC (PHYS 52015)

Term: Michaelmas Term, 2023

Submission Please submit a zip archive containing two PDF files (part1.pdf & part2.pdf)

and two code files (part1.c & part2.c).

Deadlines Consult the MISCADA learning and teaching handbook for submission deadlines.

Plagiarism and collusion Students suspected of plagiarism, either of published work or

work from unpublished sources, including the work of other students, or of collusion will be

dealt with according to Computer Science and University guidelines.

Coursework Description

Throughout the course we have considered simple programming problems largely distinct from

the typical day-to-day practice of scientific computing. In this assignment you will experience

a sliver of that practice by inheriting a codebase it is your responsibility to parallelize while

maintaining correctness.

Consider the following partial differential equation (PDE), which is a variant of the FitzHughNagumo model,

u˙ = ?2u + u(1 ? u)(u ? b) ? v, n? · ?u = 0,

v˙ = d?2

v + c(au ? v), n? · ?v = 0.

This is an example of a reaction-diffusion system — the reaction is the non-differential term

on the right-hand-side, and the diffusion is the first term on the right-hand-side. Both fields

are subject to ‘no-flux’ boundary conditions, where their normal derivative at the boundary

is identically zero. These models produce a wide array of patterns, from cardiac arrhythmias

to spots and stripes like those seen on animal coats. See here for an interactive example of

this particular model.

You will be supplied with a two-dimensional reaction-diffusion code serial.c which reads

parameters from a header file params.h, simulates the above equations, and tracks the solution

norms,

wu(t) = (δx · δy)

X

(i,j)

u(t, xi

, yj )

2

, wv(t) = (δx · δy)

X

(i,j)

v(t, xi

, yj )

2

, (1)

over time, where (i, j) ∈ [0, N)

2

range over the indices of the array.

Your assignment will be to parallelize the code using OpenMP and MPI, and to explain your

decisions with theoretically sound arguments and measurements of performance.

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Implementation Notes

? You should preserve the model parameter values and not modify params.h – only modify

the provided serial.c.

? The boundary conditions are folded into the evaluation of the diffusion term — when

i+/-1 or j+/-1 exceeds the range of u or v, then the code just mirrors these ‘ghost

points’ across the boundary back into the domain, e.g., u[-1] = u[0].

1 Your implementation should retain this behavior.

? For scaling results you should measure the executable time, rather than the time for

any subsection of the program, e.g. using the unix command time or appropriate timing

constructs covered in the course.

Part 1: OpenMP

In this assessment, you will compile and run a serial two-dimensional reaction-diffusion code,

and compare its performance against a parallelized version that you will write. The serial

code is made of five functions, init, dxdt, step, norm, and main. The expectations for your

parallel implementation are to use OpenMP #pragmas to:

? Parallelise the function init.

? Parallelise the function dxdt.

? Parallelise the function step.

? Parallelise the function norm.

Your code should be in a single C file named part1.c. Your code must compile and run

with the provided submission script, and produce the same outputs as the serial code in a file

named part1.dat.

Report

Explain and justify your parallelization strategy, using arguments based in theory covered in

the course and your scaling results. Investigate the strong scaling of your implementation.

Report scaling results using transferable metrics in your report. Additional questions you

may wish to consider in your report are listed below. Your report should be no more than

one (1) page (plus images), in a file named part1.pdf.

Questions to consider: What options for parallelisation are available? Why are some more

suitable than others? What difficulties arise in the parallelisation? Where are the necessary

synchronisation points? The solution norm requires the generation of a single output number

from an N-by-N array; what patterns are available for this function? How did you avoid data

races in your solution? Is your parallelisation approach the best option? What alternative

approaches could be used?

Part 2: MPI

In this assessment, return to the serial implementation of the two-dimensional reaction diffusion system, and parallelize the code using MPI calls, breaking down the original problem

domain into distinct regions on each process. Your implementation should:

? Reproduce the initialization of u and v across processes to match the serial code.

1See the exercise on the heat equation for a reference.

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? Correctly exchange necessary information of u and v across processes.

? Correctly calculate the norms of u and v across all ranks.

? Correctly evaluate the diffusion term on all ranks.

Your code should be a single C file called part2.c. Your code should compile and run with

the provided submission script (using 4 MPI processes), and produce the same outputs as the

serial code in a file named part2.dat.

Report

Explain and justify your parallelization strategy, using arguments based in theory covered in

the course and your scaling results. Investigate the weak scaling of your implementation.

Report scaling results using transferable metrics in your report. Additional questions you

may wish to consider in your report are listed below. Your report should be no more than

one (1) page (plus images), in a file named part2.pdf.

Questions to consider: What topologies for distribution are available with 4 MPI processes? Why might some be preferred over others? What difficulties arise in the parallelisation? The solution norm requires the generation of a single output number from an large

distributed array — what patterns are available for this problem? What if we assume that u

and/or v change slowly compared to the time-step — do any further optimizations for data

exchanges become available? What are some constraints on the possible domain sizes and

number of MPI processes for your solution?

Marking

Each part of your submission will be considered holistically, e.g. your code and report for Part

1 will be considered in tandem so that discrepancies between them will affect your marks.

Your code will be run for correctness on Hamilton. If you develop your programs on your

own machine, then you should test that it works on Hamilton with the provided submission

scripts.

Submission Points Description

All code 10 Compiles and runs to completion without errors using the provided submission scripts.

part1.c 30 Correct parallelization of the serial reaction-diffusion code using

OpenMP, producing correct outputs.

part1.pdf 20 Description and justification of parallelisation scheme, and inclusion of transferable strong scaling results.

part2.c 20 Correct parallelization of the serial reaction-diffusion model using

MPI, producing correct outputs.

part2.pdf 20 Description and justification of parallelisation scheme, and inclusion of transferable weak scaling results.

Table 1: Marking rubric for the summative coursework. Please see the report marking criteria

in the Appendix.

Submission format

Your submission should be a single zip file, uploaded to gradescope, containing part1.c,

part2.c, part1.pdf, and part2.pdf.

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Appendix

Generic coursework remarks

Stick exactly to the submission format as specified. If you alter the format (submit an archive

instead of plain files, use Word documents rather than PDFs, . . . ), the marker may refuse

to mark the whole submission. Markers will not ask for missing files. If you have to submit

code, ensure that this code does compile and, unless specified otherwise, does not require any

manual interaction. Notably, markers will not debug your code, change parameters, or assess

lines that are commented out.

All of MISCADA’s deadlines are hard deadlines: In accordance with University procedures,

submissions that are up to 5 working days late will be subject to a cap of the module pass

mark. Later submissions will receive a mark of zero. If you require an extension, please submit

an official extension request including medical evidence and/or acknowledgement by college.

Do not contact the lecturers directly, as lecturers are not entitled to grant extensions. Details

on extensions and valid reasons to grant extended deadlines can be found in the Learning

and Teaching Handbook.

It is the responsibility of the student to ensure that there are sufficient backups of their

work and that coursework is submitted with sufficient slack. Submit your coursework ahead

of time. If in doubt, submit early versions. Technical difficulties (slow internet connection

around submission deadline, lost computer hardware, accidentially deleted files, . . . ) will

not be mitigated. Please see https://www.dur.ac.uk/learningandteaching.handbook/

6/2/6/ for further information regarding illness and adverse circumstances affecting your

academic performance.

If collusion or plagiarism are detected, both students who copy and students who help to

copy can be penalised. Do not share any coursework with other students, do not assist

other students, cite all used sources incl. figures, code snippets, equations, . . . Please see

https://www.dur.ac.uk/learningandteaching.handbook/6/2/4 and https://www.dur.

ac.uk/learningandteaching.handbook/6/2/4/1 for further information.

Coursework is to be treated as private and confidential. Do not publish the whole or parts

of the coursework publicly. This includes both solutions and the plain coursework as handed

out.

Generic report quality criteria

Where summative coursework is assessed through written work in the form of a report, the

report will be assessed against some generic criteria.

The relevant grade bands (as percentages) are

0–49 Fail

50–59 Pass

60–69 Merit

70–79 Distinction

80–100 Outstanding

A fail-level report displays an unsatisfactory knowledge and understanding of the topic. The

setup and evaluation of any experimental studies is incomplete. It contains many omissions

or factual inaccuracies. Limited in scope and shows little or no evidence of critical thinking

and application of the course material to the problem. No recognition of limitations of the

approach or evaluation. Experimental data are generally presented incorrectly, or without

clarity.

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A pass-level report displays some knowledge and understanding of the topic. The setup

and evaluation of any experimental studies is competent. May contain some omissions or

factual inaccuracies. Evidence of critical thinking and application of the course material to

the problem occurs in some places. Has some recognition of limitations of the approach or

evaluation. Most experimental data are presented correctly and clearly.

A merit-level report displays good knowledge and understanding of the topic as presented

in the course material. The setup and evaluation of any experimental studies is careful and

detailed. Broadly complete in scope, with few or no errors. Evidence of critical thinking

and application of the course material to the problem is mostly clear throughout. Recognises

limitations of the approach or evaluation, and has some discussion on how to overcome them.

Experimental data are presented correctly and clearly.

A distinction-level report displays effectively complete knowledge and understanding of the

topic. The setup and evaluation of any experimental studies is well-motivated and nearflawless. Effectively no errors. Evidence of critical thinking and application of the course

material to the problem is clear throughout, and some of the discussion goes beyond the

taught material. Recognises limitations of the approach or evaluation, and presents plausible

approaches to overcome them. Experimental data are presented carefully and with attention

to detail throughout.

An outstanding-level report is similar to a distinction-level report but is effectively flawless

throughout, and shows a significant independent intellectual contribution going beyond the

taught material.

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