===affil2:
Tufts University
===firstname:
ILYA
===firstname4:

===firstname3:
Scott
===lastname2:
Adler
===keyword1:
OTHER
===lastname:
LASHUK
===firstname5:

===affil6:

===lastname3:
MacLachlan
===email:
ilya.lashuk@tufts.edu
===keyword2:
OTHER
===keyword_other2:
PDEs on surfaces
===lastname6:

===affil5:

===otherauths:

===lastname4:

===affil4:

===lastname7:

===competition:
no
===affil7:

===firstname7:

===postal:
Tufts University
School of Arts and Sciences
Department of Mathematics
Bromfield-Pearson Hall
503 Boston Avenue
Medford, MA 02155
===firstname6:

===ABSTRACT:
Numerical models of electron transport in 3D include a scattering term that, in the Fokker-Planck limit, converges to a diffusion operator on the surface of the unit sphere.  Motivated by this example, we have implemented a finite-element discretization scheme and a multilevel solver for Poisson-like PDEs on the sphere. We approximate the sphere by a piecewise-triangular surface, and the triangular faces of the approximating surface play the role of the finite elements. We are interested in the problems where the source function (nearly) has a point singularity and, thus, we use highly nonuniform meshes. Our multilevel solver is a version of the Fast Adaptive Composite Grid (FAC) method. We study numerically both the discretization accuracy and the multilevel solver performance.
===affil3:
Memorial University of Newfoundland
===keyword_other1:
FAC
===lastname5:

===affilother:

===title:
Multilevel methods for Poisson-like equations on the sphere using highly non-uniform meshes
===firstname2:
James