# Algebraic Multilevel Preconditioning in Isogeometric Analysis: Construction and Numerical Studies

Source: [Algebraic Multilevel Preconditioning in Isogeometric Analysis: Construction and Numerical Studies](<https://www.sota2.com/research/paper/68fa50761e209131ce96bb2d>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-04T05:02:01.985Z

Authors: K.P.S. Gahalaut, S.K. Tomar, J.K. Kraus

Published: 2013-04-01T17:56:09.000Z

## Abstract

We present algebraic multilevel iteration (AMLI) methods for isogeometric discretization of scalar second order elliptic problems. The construction of coarse grid operators and hierarchical complementary operators are given. Moreover, for a uniform mesh on a unit interval, the explicit representation of B-spline basis functions for a fixed mesh size $h$ is given for $p=2,3,4$ and for $C^{0}$- and $C^{p-1}$-continuity. The presented methods show $h$- and (almost) $p$-independent convergence rates. Supporting numerical results for convergence factor and iterations count for AMLI cycles ($V$-, linear $W$-, nonlinear $W$-) are provided. Numerical tests are performed, in two-dimensions on square domain and quarter annulus, and in three-dimensions on quarter thick ring.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1304.0403>)

[PDF](<https://arxiv.org/pdf/1304.0403.pdf>)