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Details of Grant 

EPSRC Reference: EP/W015439/1
Title: Parallel-in-time computation for sedimentary landscapes
Principal Investigator: Cotter, Professor C
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics
Organisation: Imperial College London
Scheme: Standard Research - NR1
Starts: 01 March 2022 Ends: 28 February 2023 Value (£): 80,620
EPSRC Research Topic Classifications:
Continuum Mechanics Mathematical Analysis
Numerical Analysis
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
29 Sep 2021 EPSRC Mathematical Sciences Small Grants Panel September 2021 Announced
Summary on Grant Application Form
This proposal is about novel mathematical techniques underpinning

computational stratigraphic models that simulate the formation of

landscapes of sedimentary rock. Sedimentary rocks form after gradual

settling of microscopic particles (formed from minerals, or coming

from plants or animals) that are suspended in ocean water. Over

millions of years, the particles settle on the ocean floor, eventually

condensing into rocks such as shale and limestone. By mathematically

modelling this process on a computer and comparing with geological

data, we can learn about the evolution of our present landscape on

Planet Earth, and we can use it to fill in the gaps between

data. These models have applications in locating carbon capture and

storage sites, and in reconstructions of recent geological history of

coral reefs, for example.

Stratigraphic models simulate the evolution of the sediment over time,

stepping from one moment in time to a later one in the near future,

executing "timesteps" one by one in a sequential manner. Accurate

modelling of the sediment processes requires that these timesteps are

0.1-1 years long. Since sedimentary landscapes form over geological

eras that are millions of years long, this means that we have to

execute millions of timesteps, one after the other. This is

prohibitively long, especially when the models are needed for data

assimilation algorithms that search for unknown properties of past

rock formation processes in the light of data obtained from geological

measurement campaigns. This is because these data assimilation

algorithms have to repeat the simulation many times with varying

parameter values. In these situations, stratigraphic modellers are

forced to use timesteps that are 1000s of years long: this yields

results of insufficient accuracy.

Our goal is to create new mathematical techniques that can make use of

highly parallel supercomputers, leading to much faster simulations and

enabling more sophisticated data assimilation algorithms to be used.

Instead of the sequential one-timestep-at-a-time approach, we will

create new algorithms that solve for all of the timesteps

simultaneously on a large number of computer processors in parallel.

We call this parallel-in-time integration. The algorithms will be

iterative, computing first guesses for the model predictions for each

timestep and then updating them until they are sufficiently

accurate. A good parallel-in-time integration method will only require

a small number of iterations, so that the result of the algorithm is

quicker than sequential computation. Finding a good parallel-in-time

integration method is a mathematical problem, with the number of

iterations being strongly dependent on the structure of the equations

that describe the simulation model. Parallel-in-time approaches have

never been investigated for stratigraphic models. In this project we

will start a new field of numerical analysis research, designing

parallel-in-time integration methods for stratigraphic models and

analysing them using a blend of theoretical analysis and high

performance computational experiments to identify the best path

forward.

Key Findings
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Organisation Website: http://www.imperial.ac.uk