# Geometry, compatibility and structure preservation in computational differential equations

Created: | 2019-07-17 14:42 |
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Institution: | Isaac Newton Institute for Mathematical Sciences |

Description: | Computations of differential equations are a fundamental activity in applied mathematics. While historically the main quest was to derive all-purpose algorithms such as finite difference, finite volume and finite element methods for space discretization, Runge–Kutta and linear multistep methods for time integration, in the last 25 years the focus has shifted to special classes of differential equations and purpose-built algorithms that are tailored to preserve special features of each class. This has given rise to the new fields of geometric numerical integration and of structure preserving discretization. In addition to being quantitatively accurate, these novel methods have the advantage of also being qualitatively accurate as they inherit the key structural properties of their continuum counterparts. This has meant a large-scale introduction of geometric and topological thinking into modern numerical mathematics.
During this scientific programme at the Isaac Newton Institute for Mathematical Sciences, we will address fundamental questions in the field of structure preserving discretizations of differential equations on manifolds in space and time. We will bring together two communities that have been pursuing their science along parallel tracks to endeavour breakthroughs in some major scientific applications, which call for advanced numerical simulation techniques. This will lead to the development of a new generation of space-time discretizations for evolutionary equations. During the programme we intend to organise three workshops and two focused study periods lasting two weeks on selected application areas. The core themes of the programme are: Compatible discretizations. Geometric numerical integration. Structure preservation and numerical relativity. Applications to computations in quantum mechanics. |

# Media items

This collection contains 74 media items.

### Media items

#### Computational Challenges in Numerical Relativity

Pretorius, F

Monday 30th September 2019 - 16:00 to 17:00

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 30 Sep 2019

#### Equivariance and structure preservation in numerical methods; some cases and viewpoints

Owren, B

Wednesday 11th December 2019 - 15:05 to 15:50

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 16 Dec 2019

#### General Relativity: One Block at a Time

Miller, W

Thursday 3rd October 2019 - 13:30 to 14:30

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 3 Oct 2019

#### Hamiltonian Monte Carlo on Homogeneous Manifolds for QCD and Statistics.

Barp, A

Thursday 21st November 2019 - 13:05 to 13:45

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 22 Nov 2019

#### Hyperbolicity and boundary conditions.

Reula, O

Tuesday 1st October 2019 - 13:30 to 14:30

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 1 Oct 2019

#### New prospects in numerical relativity

Witek, H

Wednesday 2nd October 2019 - 13:30 to 14:30

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 2 Oct 2019

#### Numerical relativity beyond astrophysics: new challenges and new dynamics

Figueras, P

Monday 30th September 2019 - 13:30 to 14:30

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 30 Sep 2019

#### Optimal control and the geometry of integrable systems

Bloch, A

Wednesday 31st July 2019 - 15:00 to 16:00

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 1 Aug 2019

#### Optimal control and the geometry of integrable systems

Bloch, A

Wednesday 31st July 2019 - 15:00 to 16:00

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 1 Aug 2019

#### Putting Infinity on the Grid

Hilditch, D

Thursday 3rd October 2019 - 11:00 to 12:00

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 3 Oct 2019

#### Some Research Problems in Mathematical and Numerical General Relativity

Holst, M

Monday 30th September 2019 - 11:00 to 12:00

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 1 Oct 2019

#### Structure-preserving time discretization: lessons for numerical relativity?

Stern, A

Monday 30th September 2019 - 14:30 to 15:30

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 30 Sep 2019

#### Tetrad methods in numerical relativity

Garfinkle, D

Friday 4th October 2019 - 16:00 to 17:00

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 4 Oct 2019

#### Variational discretizations of gauge field theories using group-equivariant interpolation spaces

Leok, M

Tuesday 1st October 2019 - 11:00 to 12:00

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 1 Oct 2019

#### A Monte Carlo method to sample a Stratification

Holmes-Cefron, M

Wednesday 20th November 2019 - 15:40 to 16:10

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 21 Nov 2019

#### A new wave-to-wire wave-energy model: from variational principle to compatible space-time discretisation

Bokhove, O

Wednesday 24th July 2019 - 15:00 to 16:00

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 24 Jul 2019

#### A Reynolds-robust preconditioner for the 3D stationary Navier-Stokes equations

Farrell, P

Thursday 31st October 2019 - 16:00 to 17:00

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 4 Nov 2019

#### A Reynolds-robust preconditioner for the 3D stationary Navier-Stokes equations

Farrell, P

Thursday 31st October 2019 - 16:00 to 17:00

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 7 Nov 2019

#### Application of the Wiener-Hopf approach to incorrectly posed BVP of plane elasticity

Galybin, A

Friday 16th August 2019 - 13:30 to 14:00

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 19 Aug 2019

#### Approximation of eigenvalue problems arising from partial differential equations: examples and counterexamples

Boffi, D

Wednesday 9th October 2019 - 15:05 to 15:50

**Collection**:
Geometry, compatibility and structure preservation in computational differential equations

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 10 Oct 2019