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- Johan Helsing, Rikard Ojala
- J. Comput. Physics
- 2008

We take a fairly comprehensive approach to the problem of solving elliptic partial differential equations numerically using integral equation methods on domains where the boundary has a large number of corners and branching points. Use of non-standard integral equations, graded meshes, interpolatory quadrature, and compressed inverse preconditioning are… (More)

- Johan Helsing, Rikard Ojala
- J. Comput. Physics
- 2008

When solving elliptic boundary value problems using integral equation methods one may need to evaluate potentials represented by a convolution of discretized layer density sources against a kernel. Standard quadrature accelerated with a fast hierarchical method for potential field evaluation gives accurate results far away from the sources. Close to the… (More)

We present a fast algorithm for the calculation of elastostatic fields in twodimensional assemblies of elastic grains, separated by sharp grain boundaries. The algorithm uses an integral equation approach, combined with the fast multipole method and recursive compression to resolve stress concentrations also very close to grain boundary junctions. Singular… (More)

- Rikard Ojala, Anna-Karin Tornberg
- J. Comput. Physics
- 2015

Article history: Received 25 June 2014 Received in revised form 12 March 2015 Accepted 1 June 2015 Available online 10 June 2015

- Rikard Ojala
- 2011

A robust and general solver for Laplace’s equation on the interior of a simply connected domain in the plane is described and tested. The solver handles general piecewise smooth domains and Dirichlet, Neumann, and Robin boundary conditions. It is based on an integral equation formulation of the problem. Difficulties due to changes in boundary conditions and… (More)

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