Patrick Diehl and Marc A. Schweitzer Efficient Neighbor Search for Particle Methods on GPUs In M. Griebel and M. A. Schweitzer, editor, Meshfree Methods for Partial Differential Equations VII, Volume 100 of Lecture Notes in Computational Science and Engineering
Chapter 5, page 81-95.
Publisher: Springer International
2014 http://dx.doi.org/10.1007/978-3-319-06898-5_5
Marc A. Schweitzer and Sa Wu Numerical Integration of on-the-fly-computed Enrichment Functions in the PUM In M. Griebel and M. A. Schweitzer, editor, Meshfree Methods for Partial Differential Equations VII, Volume 100 of Lecture Notes in Computational Science and Engineering
Chapter 13, page 247-267.
Publisher: Springer International
2014 http://dx.doi.org/10.1007/978-3-319-06898-5_13
Marc A. Schweitzer and Albert Ziegenhagel Dispersion Properties of the Partition of Unity Method & Explicit Dynamics In M. Griebel and M. A. Schweitzer, editor, Meshfree Methods for Partial Differential Equations VII, Volume 100 of Lecture Notes in Computational Science and Engineering
Chapter 14, page 269-292.
Publisher: Springer International
2014 http://dx.doi.org/10.1007/978-3-319-06898-5_14
2013
Marc A. Schweitzer Multilevel Partition of Unity Method for Elliptic Problems with Strongly Discontinuous Coefficients, Meshfree Methods for Partial Differential Equations VI In M. Griebel and M. A. Schweitzer, editor, Lecture Notes in Computational Science and Engineering, Volume 89, Meshfree Methods for Partial Differential Equations VI of Lecture Notes in Computational Science and Engineering
Chapter 6, page 93-110.
Publisher: Springer International
2013 http://dx.doi.org/10.1007/978-3-642-32979-1_6
Abstract: In this paper, we study the robustness of a multilevel partition of unity method. To this end, we consider a scalar diffusion equation in two and three space dimensions with large jumps in the diffusion coefficient or material properties. Our main focus in this investigation is if the use of simple enrichment functions is sufficient to attain a robust solver independent of the geometric complexity of the material interface.
Marc A. Schweitzer Variational Mass Lumping in the Partition of Unity Method SIAM Journal on Scientific Computing, 35(2): A1073-A1097 2013 http://dx.doi.org/10.1137/120895561
Abstract: This paper is concerned with the construction of a variational mass lumping scheme for the partition of unity methods. The presented approach is applicable to arbitrary local approximation spaces and any nonnegative partition of unity. We give improved error bounds for the partition of unity method using a nonnegative partition of unity and show that our lumped mass matrix is conservative at least for any $f \in V^{\rm PU}$ such that $f|_{\Omega\cap\omega_i} \in V_i(\omega_i)$ for all patches $\omega_i$. We present numerical results using smooth, higher order, discontinuous, and singular local approximation spaces confirming our theoretical results.