Fast solvers for frequency domain wave-scattering problems and applications

Lead Research Organisation: University of Strathclyde
Department Name: Mathematics and Statistics

Abstract

The computation of wave phenomena is widely needed in many application areas, for example models of radar and telecommunications devices require the computation of electromagnetic waves while the implementations of seismic and medical imaging algorithms use acoustic, elastic, and electromagnetic waves to obtain information about the earth's subsurface and the human body respectively.

Computer models of the propagation of waves arise naturally in the design and implementation of these technologies. Medical imaging technicians use computer models of how the material composition of the human body scatters incoming electromagnetic waves in order to solve the "inverse problem'' of reconstructing the internal makeup of a human being from an observed scattered wave field. Similarly, seismologists use computer models of how the material properties of the earth's subsurface affects the transmission of elastic waves in order to reconstruct the earth's subsurface properties from observed echoes of elastic waves

This technology is hugely useful, for example in the medical context it means we can often diagnose health problems without a need for more invasive techniques. In the seismology case it makes something seemingly impossible become possible - since it is never physically possible to explore all of the earth's subsurface properties by simply boring holes.

However the fast and accurate computer modelling of such wave phenomena is complicated and costly (in terms of computer time), principally (but not solely) because of the highly oscillatory nature of the waves and the complicated media through which they pass. Thus there is a strong need for new methods that speed up such models and that task is a principal focus of this research.

This project will devise and mathematically justify new families of fast methods for implementing these computer wave models, and will make the new methods available through two software platforms which are accessible to a wide range of scientists as well as in an additional specialist high performance computing library.

As well as devising new methods for modelling (which work well on today's multiprocessor computers), the project will also involve direct collaboration with two companies - Schlumberger (a Project Partner, interested in seismology) and ABB (interested in electromagnetic computations) - as well as two academic groups, one in geosciences and one in electromagnetics.
 
Description 1. We have analysed solvers for Maxwells equations in the high frequency regime and tested the methods on several challenging test problems showing efficiency on thousands of processors.
2. We have introduced a new two-level method for time-harmonic wave-propagation problems in frequency regime and applied this preconditioner to challenging problems from geophysics.
3. We have done extensive tests on benchmark problems and enriched the state of the art of solvers in open source software such as Freefem.
Exploitation Route The work on solvers for high frequency problems will be used by research engineers and scientists within the modern systems Freefem, HPDDM and Firedrake. These new high-performance solvers we developed will contribute (among other applications) to the numerical modelling of inverse problems in Geophysics and make available these tools to different engineering communities.
Sectors Electronics,Energy,Environment

 
Description Glasgow Mathematical Journal Trust Learning and Research Support Fund
Amount £4,000 (GBP)
Funding ID G2001-DOL 
Organisation University of Glasgow 
Department Glasgow Mathematical Journal Learning and Research Support Fund
Sector Academic/University
Country United Kingdom
Start 01/2020 
End 09/2020
 
Description LMS Conference Grants - Scheme 1
Amount £4,500 (GBP)
Funding ID 11931 
Organisation London Mathematical Society 
Sector Academic/University
Country United Kingdom
Start 08/2020 
End 09/2020
 
Description Analysis of Geneo for indefinite problems 
Organisation Heidelberg University
Country Germany 
Sector Academic/University 
PI Contribution We have engaged in substantial discussions about the performance of the GENEO preconditioner for indefinite and non-self-adjoint problems. The team of I.G. Graham and E. Spence (Bath), V. Dolean and N. Bootland (Strathclyde) and R. Scheichl and C. Ma (Heidelberg) are actively collaborating on this topic. The initial discussions took place at CIRM in Luminy at a conference whose organisers included Dr V Dolean (Strathclyde), in September 2019.
Collaborator Contribution Bath and Heidelberg are collaborating as above. Dr C. Ma will visit Bath to progress the research in March 2020 and will interact also with Niall Bootland (PDRA in Strathclude) on this topic.
Impact None as yet.
Start Year 2019
 
Description Analysis of Geneo for indefinite problems 
Organisation University of Bath
Department Department of Mathematical Sciences
Country United Kingdom 
Sector Academic/University 
PI Contribution We have engaged in substantial discussions about the performance of the GENEO preconditioner for indefinite and non-self-adjoint problems. The team of I.G. Graham and E. Spence (Bath), V. Dolean and N. Bootland (Strathclyde) and R. Scheichl and C. Ma (Heidelberg) are actively collaborating on this topic. The initial discussions took place at CIRM in Luminy at a conference whose organisers included Dr V Dolean (Strathclyde), in September 2019.
Collaborator Contribution Bath and Heidelberg are collaborating as above. Dr C. Ma will visit Bath to progress the research in March 2020 and will interact also with Niall Bootland (PDRA in Strathclude) on this topic.
Impact None as yet.
Start Year 2019
 
Description Frequency-domain seismic wave modelling based upon multi-level domain-decomposition preconditioners 
Organisation Sorbonne University
Country France 
Sector Academic/University 
PI Contribution A collaboration has been initiated with - Stéphane Operto, CNRS senior researcher at the Géoazur Laboratory (part of Observatoire de la Côte d'Azur), member of the University Côte d'Azur - Pierre-Henri Tournier, CNRS research engineer at Sorbonne University - Pierre Jolivet, CNRS junior researcher at the University of Toulouse. on the application of fast solvers to realistic geophysical problems. Two-level preconditionners developed by our team have been applied to difficult benchmark problems in frequency domain.
Collaborator Contribution Pierre-Henri Tournier and Pierre Jolivet have performed extensive tests on parallel computers to assess the performance of the method Stéphane Operto provided the benchmark problems and brought the expertise on the applications side.
Impact - The contribution we submitted to the EAGE conference (https://eage.eventsair.com/eageannual2020/), a recurrent reference European event for the geophysical community, has been accepted and will be presented on the 9th of June in Amsterdam. - The contribution we submitted to the WCCM-ECCOMAS 2020 conference (https://www.wccm-eccomas2020.org/frontal/) has been accepted and will be presented between 19-24 July in Paris.
Start Year 2019
 
Description Frequency-domain seismic wave modelling based upon multi-level domain-decomposition preconditioners 
Organisation University of Côte d'Azur
Country France 
Sector Academic/University 
PI Contribution A collaboration has been initiated with - Stéphane Operto, CNRS senior researcher at the Géoazur Laboratory (part of Observatoire de la Côte d'Azur), member of the University Côte d'Azur - Pierre-Henri Tournier, CNRS research engineer at Sorbonne University - Pierre Jolivet, CNRS junior researcher at the University of Toulouse. on the application of fast solvers to realistic geophysical problems. Two-level preconditionners developed by our team have been applied to difficult benchmark problems in frequency domain.
Collaborator Contribution Pierre-Henri Tournier and Pierre Jolivet have performed extensive tests on parallel computers to assess the performance of the method Stéphane Operto provided the benchmark problems and brought the expertise on the applications side.
Impact - The contribution we submitted to the EAGE conference (https://eage.eventsair.com/eageannual2020/), a recurrent reference European event for the geophysical community, has been accepted and will be presented on the 9th of June in Amsterdam. - The contribution we submitted to the WCCM-ECCOMAS 2020 conference (https://www.wccm-eccomas2020.org/frontal/) has been accepted and will be presented between 19-24 July in Paris.
Start Year 2019
 
Description Frequency-domain seismic wave modelling based upon multi-level domain-decomposition preconditioners 
Organisation University of Toulouse
Country France 
Sector Academic/University 
PI Contribution A collaboration has been initiated with - Stéphane Operto, CNRS senior researcher at the Géoazur Laboratory (part of Observatoire de la Côte d'Azur), member of the University Côte d'Azur - Pierre-Henri Tournier, CNRS research engineer at Sorbonne University - Pierre Jolivet, CNRS junior researcher at the University of Toulouse. on the application of fast solvers to realistic geophysical problems. Two-level preconditionners developed by our team have been applied to difficult benchmark problems in frequency domain.
Collaborator Contribution Pierre-Henri Tournier and Pierre Jolivet have performed extensive tests on parallel computers to assess the performance of the method Stéphane Operto provided the benchmark problems and brought the expertise on the applications side.
Impact - The contribution we submitted to the EAGE conference (https://eage.eventsair.com/eageannual2020/), a recurrent reference European event for the geophysical community, has been accepted and will be presented on the 9th of June in Amsterdam. - The contribution we submitted to the WCCM-ECCOMAS 2020 conference (https://www.wccm-eccomas2020.org/frontal/) has been accepted and will be presented between 19-24 July in Paris.
Start Year 2019
 
Description Solvers for Full Waveform Inversion 
Organisation University of Bath
Country United Kingdom 
Sector Academic/University 
PI Contribution A team from Bath (I.G. Graham, S. Gazzola, E.A. Spence) and V. Dolean (Strathclyde) travelled to Nice in October 2019 to meet the team of Geophysicists headed by Prof S. Operto. We had intensive discussions about fast solvers and novel inverse solvers in the context of FWI.
Collaborator Contribution Professor Operto's team (Nice) provided a 2 day discussion session on FWI and related problems. I.G. Graham and E.A. Spence provided expertise on fast solvers and S. Gazzola on inverse problems in the discussion.
Impact None as yet.
Start Year 2019
 
Description Solvers for Full Waveform Inversion 
Organisation University of Côte d'Azur
Country France 
Sector Academic/University 
PI Contribution A team from Bath (I.G. Graham, S. Gazzola, E.A. Spence) and V. Dolean (Strathclyde) travelled to Nice in October 2019 to meet the team of Geophysicists headed by Prof S. Operto. We had intensive discussions about fast solvers and novel inverse solvers in the context of FWI.
Collaborator Contribution Professor Operto's team (Nice) provided a 2 day discussion session on FWI and related problems. I.G. Graham and E.A. Spence provided expertise on fast solvers and S. Gazzola on inverse problems in the discussion.
Impact None as yet.
Start Year 2019
 
Description Two-level solvers for Helmholtz problems 
Organisation Delft University of Technology (TU Delft)
Country Netherlands 
Sector Academic/University 
PI Contribution During an event organised by the University of Strathclyde "International Strategic Partnerships Strathclyde/TU Delft scoping workshop" Ross Priory, 20/21 November 2019, a discussion has been initiated with Prof. Kees Vuik from the University of Delft and a collaboration has started soon after on the development of two-level methods for Helmholtz equations. Researchers involved: Kees Vuik, Vandana Dwarka (Phd Student in Delft), V. Dolean and N. Bootland (University of Strathclyde).
Collaborator Contribution Kees Vuik, Vandana Dwarka (TU Delft) and V. Dolean, N. Bootland (Strathclyde) have planned to meet at the Iterative methods conference in Copper Mountain (March 2020) to progress the research. A working plan has been set up and partners from Delft will apply their method on data (from in-house numerical simulation codes) provided by Strathclyde.
Impact None as yet
Start Year 2019
 
Description Parallel Solution Methods for Systems Arising from PDEs 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact V. Dolean was one of the organisers of the international workshop "Parallel Solution Methods for Systems Arising from PDEs" which took place in CIRM (International Centre of Mathematical Meetings) in Marseille from 16-20 September 2019. This meeting gathered around 60 participants, well known international researchers in the broad field of parallel iterative solvers. Four others members of our EPSRC project took part in this meeting (I.G. Graham, S. Gong, N. Bootland and A. Kyriakis) which contributed to active exchanges and to setting plans and new collaborations for the future research activity.
Year(s) Of Engagement Activity 2019
 
Description Stakeholders meeting for this project 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Industry/Business
Results and Impact On October 7 2019, in collaboration with Prof. Ivan G. Graham from Bath, we have organised the first Stakeholders meeting for our grant. Attendees included industrialists from Schlumberger and ABB, software developers from Imperial College and Toulouse as well as the academic members, collaborators of the project, PDRAs and research students from our teams (Strathclyde and Bath).
Year(s) Of Engagement Activity 2019