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Full-Text Articles in Applied Mathematics
A Node Elimination Algorithm For Cubatures Of High-Dimensional Polytopes, Arkadijs Slobodkins
A Node Elimination Algorithm For Cubatures Of High-Dimensional Polytopes, Arkadijs Slobodkins
Mathematics Theses and Dissertations
Node elimination is a numerical approach for obtaining cubature rules for the approximation of multivariate integrals over domains in Rn. Beginning with a known cubature, nodes are selected for elimination, and a new, more efficient rule is constructed by iteratively solving the moment equations. In this work, a new node elimination criterion is introduced that is based on linearization of the moment equations. In addition, a penalized iterative solver is introduced that ensures positivity of weights and interiority of nodes. We aim to construct a universal algorithm for convex polytopes that produces efficient cubature rules without any user …
Practical Implementation Of The Immersed Interface Method With Triangular Meshes For 3d Rigid Solids In A Fluid Flow, Norah Hakami
Practical Implementation Of The Immersed Interface Method With Triangular Meshes For 3d Rigid Solids In A Fluid Flow, Norah Hakami
Mathematics Theses and Dissertations
When employing the immersed interface method (IIM) to simulate a fluid flow around a moving rigid object, the immersed object can be replaced by a virtual fluid enclosed by singular forces on the interface between the real and virtual fluids. These forces represent the impact of the rigid motion on the fluid flow and cause jump discontinuities across the interface in the whole flow field. Then, the IIM resolves the fluid flow on a fixed computational domain by directly incorporating the jump conditions across the interface into numerical schemes. Previous development of the method is limited to simple smooth boundaries. …