89 Results Found

This article presents single- and multi-disciplinary shape optimizations of a generic business jet wing at two transonic cruise flow conditions. The studies performed are based on two high-fidelity gradient-based optimization tools, assisted by the a...

In this paper, the continuous adjoint method is used for the optimization of a static mixing device. The CFD model used is suitable for the flow simulation of the two miscible fluids that enter the device. The formulation of the adjoint equations, wh...

This paper presents an adjoint-based shape optimization framework and its demonstration in a conjugate heat transfer problem in a turbine blading. The gradient of the objective function is computed based on the continuous adjoint method, which also i...

This paper presents a topology optimization (TopO) method for conjugate heat transfer (CHT), with turbulent flows. Topological changes are controlled by an artificial material distribution field (design variables), defined at the cells of a backgroun...

Jet centrifugal pumps frequently suffer from low energy conversion efficiency due to severe fluid mixing and inter-stage interference. To address this, a structural optimization framework combining the continuous adjoint method and machine learning i...

The adjoint method is a very promising gradient-based optimisation framework for computational fluid dynamics (CFD), because of its independence of the computation cost from the number of design variables. With the aim of improving the robustness of...

A continuous adjoint-based aeroacoustic optimization, based on a hybrid model including the Ffowcs Williams–Hawkings (FW–H) acoustic analogy, to account for the multidisciplinary design of aero-engine intakes with an axisymmetric geometry...

Efficient Robust Design Optimization (RDO) strategies coupling a parsimonious uncertainty quantification (UQ) method with a surrogate-based multi-objective genetic algorithm (SMOGA) are investigated for a test problem in computational fluid dynamics...

In this paper we study the existence of a mild solution of a periodic boundary value problem for fractional quasilinear differential equations in a Hilbert spaces. We assume that a linear part in equations is a self-adjoint positive operator with den...

Much work has been done over the past years to obtain a better understanding, predict and alleviate the effects of cavitation on the performance of lifting surfaces for hydrokinetic turbines and marine propellers. Lifting-surface sheet cavitation, wh...

Drag sensitivities quantify how changes in rheological parameters affect the force on a confined body. Continuous adjoints are implemented with finite volumes for creeping Carreau flow and low-Reynolds-number Oldroyd-B flow past cylinders. The Carrea...

The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D steady-state Euler equations and the first goal of this...

In the last decade, parameter-free approaches to shape optimization problems have matured to a state where they provide a versatile tool for complex engineering applications. However, sensitivity distributions obtained from shape derivatives in this...

This paper considers the formulation of the adjoint problem in two dimensions when there are shocks in the flow solution. For typical cost functions, the adjoint variables are continuous at shocks, wherein they have to obey an internal boundary condi...

We consider an operator ${\{S\left(t\right)\}}_{t\ge 0}$ on a Banach space X with generator A, characterized by being an $\alpha$-times-integrated C-regularized semigroup. The adjoint family $S^{*}\left(t\right):X^{*}\to X^{*}$ is introduced for analysis. ${\{S^{*}\left(t\right)\}}_{t\ge 0}$ maintains the charact...

The continuous adjoint approach is a technique for calculating the sensitivity of a flow to changes in input parameters, most commonly changes of geometry. Here we present for the first time the mathematical derivation of the adjoint system for multi...

The adjoint approach in gradient-based optimization combined with computational fluid dynamics is commonly applied in various engineering fields. In this work, the gradients are used for the design of a two-dimensional airfoil shape, where the aim is...

This paper investigates Parseval–Goldstein-type relationships in the framework of Lebedev–Skalskaya transforms. The research also examines the continuity properties of these transforms, along with their adjoint counterparts over weighted...

In a previous paper, we used a classification of the self adjoint extensions, also called self-adjoint determinations, of the differential operator $-d^2/d{x}^2$ in order to obtain the whole list of Supersymmetric (SUSY) partners of those selfadjoint...

Fractional calculus provides tools to model systems with memory effects; when coupled with delays, they model process histories inspired by two independent sources—the memory of the fractional derivative and the impact conditioned by the delays. This...

Suppose X and Y are Banach spaces, K is a compact Hausdorff space, and $C(K, X)$ is the Banach space of all continuous X-valued functions (with the supremum norm). We will study some strongly bounded operators $T:C(K, X)\to Y$ with representi...

The adjoint function of connection number has unique advantages in solving uncertainty problems of water resource complex systems, and has become an important frontier and research hotspot in the uncertainty research of water resource complex problem...

Modal expansions based on k-eigenvalues and α-eigenvalues are commonly used in order to investigate the reactor behaviour, each with a distinct point of view: the former is related to fission generations, whereas the latter is related to time. Well-k...

The applicability of adjoint-based gradient computation is investigated in the context of interfacial flows. Emphasis is set on the approximation of the transport of a characteristic function in a potential flow by means of an algebraic volume-of-flu...

The inverse or cathode shape design problem of electrochemical machining (ECM) deals with the computation of the shape of the tool cathode required for producing a workpiece anode of a desired shape. This work applied the complex variable method and...

Reverse time migration (RTM) exploits time-reversal symmetry and adjoint duality to focus wavefields and reconstruct subsurface reflectivity, but large surveys remain limited by the cost of forward and backward propagation. We present a Graphics Proc...

Recently, a new class of operators called $⟨\mathbf{A}⟩$-normal operators was introduced. These operators satisfy the identity $\mathbf{A}\mathcal{T}{\mathcal{T}}^{{♯}_{\mathbf{A}}}=\mathbf{A}{\mathcal{T}}^{{♯}_{\mathbf{A}}}\mathcal{T}$, where $\mathbf{A}$ is a positive semi-definite operator on a complex Hilbert space $\mathcal{K}$, $\mathcal{T}$ is a bounded linear operator that...

The purpose of this article is to investigate some tensorial norm inequalities for continuous functions of self-adjoint operators in Hilbert spaces. Our first approach is to develop a gradient descent inequality and some relational properties for con...

Wing topology optimization often uses different aerodynamic and structural meshes, and the effect of the load transfer and of load errors on the optimum is rarely quantified. We study both for a fixed wing shape under one-way panel-method loads. The...

In this paper, various tensorial inequalities of trapezoid type were obtained. Identity from classical analysis is utilized to obtain the tensorial version of the said identity which in turn allowed us to obtain tensorial inequalities in Hilbert spac...

This research work introduces a connection of adjoint Bernoulli’s polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators are investigated in various funct...

In this paper, we introduce a discretization scheme for the Yang–Mills equations in the two-dimensional case using a framework based on discrete exterior calculus. Within this framework, we define discrete versions of the exterior covariant der...

In this work, we first establish a new connection between adjoint Bernoulli’s polynomials and gamma function as a new sequence of linear positive operators denoted by ${\mathfrak{S}}_{r,\varsigma ,\lambda }(.;.)$. Further, convergence results for these sequences o...

This article presents a gradient-based aerodynamic optimization framework and investigates optimum deformations for a transonic airfoil equipped with morphing leading and trailing edges. Specifically, the proposed optimization framework integrates an...

This paper introduces a rigorously defined fractional Heun operator constructed through a symmetric composition of left and right Riemann–Liouville fractional derivatives. By deriving a compatible fractional Pearson-type equation, a new weight...

This paper investigates a multi-objective optimization framework for the simultaneous parameter identification and optimal vaccination control of a generalized non-linear SIR epidemic model. In contrast to traditional single-objective approaches, we...

This is a pedagogical introduction to the physics of confinement on $R^3\times S^1$, using $SU\left(2\right)$ Yang–Mills with massive or massless adjoint fermions as the prime example; we also add fundamental flavours to conclude. The small-$S^1$ limit is remarkab...

This paper is dedicated to exploring the existence, uniqueness and Ulam stability analysis applied to a specific class of mathematical equations known as nonlinear impulsive Volterra Fredholm integro-dynamic adjoint equations within finite time scale...

We establish a version of Pontryagin’s maximum principle for optimal control problems with impulses and phase constraints. Using the Dubovitskii–Milyutin theory, we construct a conic variational framework that handles impulsive dynamics a...

This work constructs an orthogonal function system on bounded intervals $[0,R]$ associated with the Atangana–Baleanu–Caputo (ABC) fractional derivative for $\alpha \in (1/2,1)$. Starting from a fractional Laguerre-type equation involving th...

We continue the study of a non-self-adjoint fractional three-term Sturm–Liouville boundary value problem (with a potential term) formed by the composition of a left Caputo and left Riemann–Liouville fractional integral under Dirichlet typ...

The first aim of this study is to point out new aspects of approximation theory applied to a few classes of holomorphic functions via Vitali’s theorem. The approximation is made with the aid of the complex moments of the functions involved, whi...

The existence and uniqueness of a local solution is proved for the incomplete Cauchy type problem to multi-term quasilinear fractional differential equations in Banach spaces with Riemann–Liouville derivatives and bounded operators at them. Non...

In this paper, we study a kind of Stackelberg game where the controlled systems are described by backward stochastic differential delayed equations (BSDDEs). By introducing a new kind of adjoint equation, we establish the sufficient verification theo...

We study Gamma ratios evaluated at a shifted square root and finite products of their positive powers. For each ratio, we prove the complete Bernstein property and compute the representing measure explicitly. The symmetry of the Gamma parameters give...

The technique of machine learning has been increasingly applied in numerical weather predictions. The aim of this study is to explore the application of a neural network in data assimilation by making use of the convenience in obtaining the tangent l...

Frequency stability becomes more and more important with the increase in inverter-based resources in power systems. To enhance the frequency stability, this paper proposes a novel data-driven method for frequency stability assessment and control for...

The paper presents k-version of the finite element method for boundary value problems (BVPs) and initial value problems (IVPs) in which global differentiability of approximations is always the result of the union of local approximations. The higher o...

The Monte Carlo neutron transport method is used to accurately estimate various quantities, such as k-eigenvalue and integral neutron flux. However, in the case of estimating a distribution of a desired quantity, the Monte Carlo method does not typic...

We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special functions se...