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A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, E. Vanden-Eijnden, An ...
In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of th ...
Isogeometric analysis (IGA) is a computational methodology recently developed to numerically approximate Partial Differential Equation (PDEs). It is based on the isogeometric paradigm, for which the same basis functions used to represent the geometry are t ...
Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...
A numerical algorithm that achieves asymptotic stability for feedback linearizable systems is presented. The nonlinear systems can be represented in various forms that include differential equations, simulated physical models or lookup tables. The proposed ...
In this paper we report a fundamental morphological instability of constrained 3D microtissues induced by positive chemomechanical feedback between actomyosin-driven contraction and the mechanical stresses arising from the constraints. Using a 3D model for ...
We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of It stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are show ...
In this thesis, we study several stochastic partial differential equations (SPDE’s) in the spatial domain R, driven by multiplicative space-time white noise. We are interested in how rough and unbounded initial data affect the random field solution and the ...
Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrat ...
In this work, we present a complete derivation of the NonAdiabatic Bohmian DYnamics (NABDY) equations of motion. This approach naturally emerges from a transformation of the molecular time-dependent Schrodinger equation in the adiabatic representation of t ...