In the variational data assimilation (VarDA), the typical way for gradient computation is using the adjoint method. However, the adjoint method has many problems, such as low accuracy, difficult implementation and considerable complexity, for high-dimensional models. To overcome these shortcomings, a new data assimilation method based on dual number automatic differentiation (AD) is proposed. T...

We propose an image-domain velocity model building method using the two-way wave equation and extended seismic images. We show that common-image-point gathers can effectively extract velocity information from steep reflections imaged with the two-way wave propagator. Such gathers have the advantages over conventional common-image gathers that they are capable of characterizing reflections with ...

This note is a first attempt to perform waveform inversion by utilizing recent developments in semidefinite relaxations for polynomial equations to mitigate non-convexity. The approach consists in reformulating the inverse problem as a set of constraints on a low-rank moment matrix in a higher-dimensional space. While this idea has mostly been a theoretical curiosity so far, the novelty of this...

In this paper we present an approach to shape optimization which is based on continuous adjoint computations. If the exact discrete adjoint equation is used, the resulting formula yields the exact discrete reduced gradient. We first introduce the adjoint-based shape derivative computation in a Banach space setting. This method is then applied to the instationary NavierStokes equations. Finally,...

In this paper we give an effective method for finding a unique representative of each orbit of the adjoint and coadjoint action of the real affine orthogonal group on its Lie algebra. In both cases there are orbits which have a modulus that is different from the usual invariants for orthogonal groups. We find an unexplained bijection between adjoint and coadjoint orbits. As a special case, we c...

Spectral stability analysis for solitary waves is developed in the context of the Hamiltonian system of coupled nonlinear Schrödinger equations. The linear eigenvalue problem for a non-self-adjoint operator is studied with two self-adjoint matrix Schrödinger operators. Sharp bounds on the number and type of unstable eigenvalues in the spectral problem are found from the inertia law for quadrati...

We propose an ensemble sensitivity method to calculate observation impacts similar to Langland and Baker (2004) but without the need for an adjoint model, which is not always available for numerical weather prediction models. The formulation is tested on the Lorenz 40-variable model, and the results show that the observation impact estimated from the ensemble sensitivity method is similar to th...

application of backward probability method in pollutant source tracking in non-uniform flow riversalireza ghanem.sc. student of water structures, tarbiat modares university, tehranmehdi mazaheri assistant prof., department of water structures, tarbiat modares university, tehranjamal mohammad vali samaniprofessor, department of water structures, tarbiat modares university, tehranintroductionriv...

This paper presents an accurate and efficient full-wave method, combined with iterative adjoint technique, for analyzing sensitivities of planar microwave circuits with respect to design parameters. Method of moments (MoM) in spatial domain is utilized, and generalized conjugate residual iterative scheme is applied to solve the linear matrix equations with fast convergence. Green’s functions fo...

The objective of this note is to show how one can combine Polynomial Chaos Expansions (PCE) and adjoint theory to efficiently obtain sensitivities for robust optimal control. A non-intrusive PCE method is used to analyze the constraint equations for the state (which depends on uncertain inputs), namely the governing equations of the dynamical system. Adjoint solutions are constructed for each o...