The Laplace operator admits infinite self-adjoint extensions when considered on a segment of the real line. They have different domains of essential self-adjointness characterized by a suitable set of boundary conditions on the wave functions. In this paper we show how to recover these extensions by studying the continuum limit of certain discretized versions of the Laplace operator on a lattic...

We propose an efficient PDE based approach for solving the first-arrival traveltime tomography problem in irregular domains. consider mismatch functional on $L_1$ or $L_2$ fidelity term, respectively, and we compute both gradients with respect to sound speed by adjoint-state method. The novelty of proposed method consists two aspects. First, since is formulated domain, develop new level-set fas...

— This paper proposes a method for optimal dynamic control of nonlinear time-invariant systems with a quadratic performance criterion by using the adjoint formulation of the system. From the Lagrangian the adjoint system is derived in terms of the Lagrange Multipliers, which are also called costate variables. Our approach makes the elimination of the costate possible and provides a dynamic cont...

Adjoint sensitivity analysis is used to study the New York Bight circulation for three idealized situations: an unforced buoyant river plume, and upwelling and downwelling wind forcing. A derivation of adjoint sensitivity is presented that clarifies how the method simultaneously addresses initial, boundary, and forcing sensitivities. Considerations of interpretation and appropriate definitions ...

The paper presents an adjoint based approach for determining global error in the time domain that is relevant to functional outputs from unsteady flow simulations. The algorithm is derived for the unsteady Euler equations that are discretized for second-order accuracy in both space and time and takes into account the effect of dynamic meshes. In addition to error due to temporal resolution, the...

This paper deals with the convergence analysis of various preconditioned iterations to compute the smallest eigenvalue of a discretized self-adjoint and elliptic partial differential operator. For these eigenproblems several preconditioned iterative solvers are known, but unfortunately, the convergence theory for some of these solvers is not very well understood. The aim is to show that precond...

in this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time- dependent heat flux using the temperature distribution at a point in a three layer system with none homogeneous boundary conditions. also, the effect of noisy data on final solution is studied. for solving this problem the general co...

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...

In topology optimization, the state of structures is typically obtained by numerically evaluating a discretized PDE-based model. The degrees freedom such model can be partitioned in free and prescribed sets to define boundary conditions. A multi-partition problem involves multiple partitions same discretization, corresponding different loading scenarios. As result, solving problems factorizatio...