L. Quevedo

Parallel Fast Multipole Boundary Element Method for crustal dynamics

Crustal faults and sharp material transitions in the crust are usually represented as triangulated surfaces in structural geological models. The complex range of volumes separating such surfaces is typically three-dimensionally meshed in order to solve equations that describe crustal deformation with the finite-difference (FD) or finite-element (FEM) methods. We show here how the Boundary Element Method, combined with the Multipole approach, can revolutionise the calculation of stress and strain, solving the problem of computational scalability from reservoir to basin scales. The Fast Multipole Boundary Element Method (Fast BEM) tackles the difficulty of handling the intricate volume meshes and high resolution of crustal data that has put classical Finite 3D approaches in a performance crisis. The two main performance enhancements of this method: the reduction of required mesh elements from cubic to quadratic with linear size and linear-logarithmic runtime; achieve a reduction of memory and runtime requirements allowing the treatment of a new scale of geodynamic models. This approach was recently tested and applied in a series of papers by [1, 2, 3] for regional and global geodynamics, using KD trees for fast identification of near and far-field interacting elements, and MPI parallelised code on distributed memory architectures, and is now in active development for crustal dynamics. As the method is based on a free-surface, it allows easy data transfer to geological visualisation tools where only changes in boundaries and material properties are required as input parameters. In addition, easy volume mesh sampling of physical quantities enables direct integration with existing FD/FEM code.

Ascent of bubbles in magma conduits using boundary elements and particles

Abstract We investigate the use of the Multipole-accelerated Boundary Element Method (BEM) and of the Singularity Method for studying the interaction of many bubbles rising in a volcanic conduit. Observation shows that the expression of volcanic eruption is extremely variable, from slow release of magma to catastrophic explosive manifestation. We investigate the application of the Fast Multipole Method to the solution of (i) the Boundary Element Formulation of the Stokes flow and of (ii) the particle formulation using the Stokeslets, the Green Function of the Stokes flow law, as a particle kernel. We show how these implementations allow for the first time to numerically model in a dynamic setting a very large number of bubbles, i.e few thousands with the BEM models, allowing investigating the feedback between the single bubble deformation and their collective evolution, and few hundred of thousands of bubbles with the particle approach. We illustrate how this method can be used to investigate the intense interaction of a large number of bubbles and suggest a framework for studying the feedback between many bubbles and a complex thermal nonlinear magmatic