129 citations · 316 across the 45 of their papers we have counts for
8 papers · 1 filter
Derivation of resonance-based schemes via normal forms
Yvain Bruned
In this work, we propose a systematic derivation of resonance-based schemes via normal forms. The main idea is to use an arborification map on decorated trees together with a Butch…
Elementary differentials from multi-indices to rooted trees
Yvain Bruned, Paul Laubie
Rooted trees are essential for describing numerical schemes via the so-called B-series. They have also been used extensively in rough analysis for expanding solutions of singular S…
Birkhoff normal form via decorated trees
Jacob Armstrong-Goodall, Yvain Bruned
We derive an explicit tree based ansatz for the Birkhoff normal form up to any order in the context of Hamiltonian PDEs. To do so we make use of a tree based representation of iter…
Post-Lie deformations of pre-Lie algebras and their applications in Regularity Structures
Yvain Bruned, Yunhe Sheng, Rong Tang
In this paper, we study post-Lie deformations of a pre-Lie algebra, namely deforming a pre-Lie algebra into a post-Lie algebra. We construct the differential graded Lie algebra tha…
Resonances and computations
Yvain Bruned, Frédéric Rousset, Katharina Schratz
The computation of time dynamics arising in nonlinear time-dependent partial differential equations is an ongoing challenge in numerical analysis, especially once roughness comes i…
Renormalisation in the flow approach for singular SPDEs
Yvain Bruned, Aurélien Minguella
In this work, we study the renormalisation of singular SPDEs in the flow approach recently developed by Duch. We introduce a general ansatz based on decorated trees for the solutio…
Flows driven by multi-indices Rough Paths
Carlo Bellingeri, Yvain Bruned, Yingtong Hou
In this work, we introduce a solution theory for scalar-valued rough differential equations driven by multi-indices rough paths. To achieve this task, we will show how the flow app…
Renormalising Feynman diagrams with multi-indices
Yvain Bruned, Yingtong Hou
In this work, we provide a method to obtain the renormalised measure in quantum field theory directly from the renormalisation of the expansion of the original measure. Our approac…