New directions in applied linear algebra, numerical methods for PDEs, and applications
Apr 09, 2018 - Apr 11, 2018
ICMS, 15 South College Street, Edinburgh, EH8 9AA
|Pearson, John||University of Edinburgh|
The accurate numerical solution of partial differential equations and optimization problems, including through the use of linear algebra techniques for solving the resulting matrix systems, presents vast challenges for researchers in applied mathematics and engineering. In this workshop, we consider the fast and efficient discretization and solution of PDEs arising from a wide variety of scientific applications, including optimization problems where PDEs act as constraints.
This workshop will consist of presentations from a number of leading researchers, aimed to encourage an exchange of ideas to further advance the state of the art in the numerical solution of PDEs, applied linear algebra, and computational optimization.
Dr Silvia Gazzola, University of Bath,
Dr Ben Goddard, University of Edinburgh
Dr Stefan Güttel, University of Manchester,
Dr John Pearson, University of Edinburgh
Dr Margherita Porcelli, Università degli Studi di Firenze
Dr Tyrone Rees, Rutherford Appleton Laboratory
Dr Carola Schönlieb, University of Cambridge
Prof Jennifer Scott, Rutherford Appleton Laboratory & University of Reading
Prof Zdenek Strakos, Charles University in Prague
Prof Walter Zulehner, Johannes Kepler University Linz
Please note that this workshop is anticipated to commence around lunchtime on Monday 9 April until around 17:00 on Wednesday 11 April 2018. Please take this into account when planning your travel arrangements.
Participation is by invitation only. Speaker Invitations will be issued by ICMS in January 2018. All other invitees will be sent out at the end of February 2018.
The workshop will be held at ICMS, 15 South College Street, Edinburgh.
TALKS AND AUDIO/VISUAL EQUIPMENT
All talks will be held in the Newhaven Lecture Theatre. The lecture theatre has a built in computer, data projector, and visualiser/document camera. In addition, there are two blackboards. The projector and one board may be used simultaneously. We advise Speakers that, where possible, you bring your talk on a memory stick/USB to put onto our computer in advance of your session - either at the start of the day or during coffee/lunch breaks. ICMS staff can help with this. It is possible for you to use your own laptops but it is then your own responsibility to ensure that resolutions are changed on the laptops if necessary (ICMS will not change the resolution on our equipment). If you use a MAC we expect you to bring your own adaptor.
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one.
Information about travel to the UK and Edinburgh is available here.
Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies that may occur on your trip.
A taxi directly from the airport will cost approximately 20.00 to 25.00 GBP to the city centre for a one-way journey. There is also a bus service direct from the airport to the city centre which will cost 4.50 GBP single or 7.50 GBP return - the Airlink 100. This is a frequent service (every 10 minutes during peak times) and will bring you close to Waverley Railway Station, only a short walk to the accommodation and the workshop venue (see map in 'Venue' section above).
Lothian buses charge £1.60 for a single, £4.00 for a day ticket. Please note that the exact fare is required and no change is given.
If travelling by train, please note that Edinburgh has several railway stations - Waverley Railway Station being the main station and closest to the workshop venue at 15 South College Street. If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk over North and South Bridge. The second large railway station is called Haymarket and is at the West End of the city centre. Please be aware that there is also an Edinburgh Park railway station but this is at the west side of the city some way from the city centre. For ICMS, use Edinburgh Waverley.
Administrative enquiries regarding practical arrangements in Edinburgh should be emailed to: moira (dot) firstname.lastname@example.org
|Recent advances in iterative regularization methods|
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|Pseudospectral methods for integro-PDEs|
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Motivated by applications in statistical mechanics and fluid dynamics, we propose a novel, efficient pseudospectral collocation scheme for non-local, non-linear, integro-PDEs. In particular, we compute the non-local, integral terms in real space with the help of a specialised Gauss quadrature. Due to the exponential accuracy of the quadrature, and a convenient choice of collocation points near interfaces, we can use grids with a significantly lower number of nodes than most other reported methods. In addition, the method can be directly applied to both (non-periodic) bounded and unbounded domains. We demonstrate the effectiveness of the scheme by applying it to examples from soft matter and complex fluids.
Joint work with Serafim Kalliadasis, Andreas Nold, Nikos Savva and Peter Yatsyshin.
|Decomposition into subspaces and operator preconditioning|
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|We will consider linear equations in the abstract infinite-dimensional Hilbert space setting with bounded, coercive and self-adjoint operators, which can represent, e.g., boundary value problems formulated via partial differential equations. Efficient numerical solution procedures often incorporate transformation of the original problem using preconditioning. Motivated, in particular, by the works of several authors published in the early 90's, this text will present an abstract formulation of operator preconditioning based on the idea of decomposition of a Hilbert space into a finite number of (infinite-dimensional) subspaces with focusing on the concepts of norm equivalence and spectral equivalence of infinite-dimensional operators. The goal is to describe in a concise way the common principles behind various computational techniques using infinite-dimensional function spaces.|
|Gazzola, Silvia||University of Bath|
|Goddard, Ben||University of Edinburgh|
|Gondzio, Jacek||University of Edinburgh|
|Strakos, Zdenek||Charles University, Prague|