This paper proposes an approach that combines manual differentiation (MD) and automatic differentiation (AD) to develop an efficient and accurate multi-row discrete adjoint solver. In this approach, the structures of adjoint codes generated using an...
Reducing fuel consumption and improving the economy by effectively reducing cruising drag is the main objective of the aerodynamic design of supersonic civil aircraft. In this paper, the aerodynamic optimization design system based on the Reynolds-Av...
This paper presents an optimisation framework based on an open-source CAD system and CFD solver. In this work, the high-fidelity flow solutions and surface sensitivities are obtained using the primal and discrete adjoint formulations of
In actual flight, aircraft rarely operate under a single design condition; multiple flight states must be considered to meet performance requirements. With the push for green and low-carbon aviation, there is growing demand for high-performance, fuel...
A direct approach is proposed for constructing conservation laws of discrete evolution equations, regardless of the existence of a Lagrangian. The approach utilizes pairs of symmetries and adjoint symmetries, in which adjoint symmetries make up for t...
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...
This paper introduces a low-boom aircraft optimization design method guided by equivalent area distribution, which effectively improves the intuitiveness and refinement of inverse design. A gradient optimization method based on discrete adjoint equat...
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...
25 November 2020
This paper addresses the problem of the design optimization of turbomachinery components under thermo-mechanical constraints, with focus on a radial turbine impeller for turbocharger applications. Typically, turbine components operate at high tempera...
This paper is concerned with the construction and convergence analysis of novel implicit Peer triplets of two-step nature with four stages for nonlinear ODE constrained optimal control problems. We combine the property of superconvergence of some sta...
This paper focuses on the construction of the Jacobian matrix required in tomographic reconstruction algorithms. In microwave tomography, computing the forward solutions during the iterative reconstruction process impacts the accuracy and computation...
The discrete adjoint method was used to optimize the aerodynamic configuration in order to increase the efficiency and precision of design. The fully unstable simulation of propeller rotation was avoided using the quasi approach. In the meantime, the...
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...
DC short-circuit faults are one of the challenges for modular multilevel converter (MMC) based DC grid. It is vital for proper design of protection system to estimate the fault currents and voltages. The existing calculation methods based on RLC equi...
Robust optimization design (ROD) is playing an increasingly significant role in aerodynamic shape optimization and aircraft design. However, an efficient ROD framework that couples uncertainty quantification (UQ) and a powerful optimization algorithm...
We discuss quantum time states formed with a finite number of energy eigenstates with the purpose of obtaining a time coordinate. These time states are eigenstates of the recently introduced discrete time operator. The coordinate and momentum represe...
We define a finite-differences derivative operation, on a non uniformly spaced partition, which has the exponential function as an exact eigenvector. We discuss some properties of this operator and we propose a definition for the components of a fini...
Flow topology optimization (TopOpt) based on Darcy’s source term is widely used in the field of TopOpt. It has a high degree of freedom, making it suitable for conceptual aerodynamic design. Two problems of TopOpt are addressed in this paper to...
In this paper, the time fractional diffusion equations optimal control problem is solved by
In this paper, the streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for optimal control problem governed by a convection dominated diffusion equation is investigated. The virtual element discrete scheme is constructed...
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...
Optimization using finite element analysis and the adjoint variable method to solve engineering problems appears in various application areas. However, to the best of the authors’ knowledge, there is a lack of detailed explanation on the implem...
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 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...
We find supersymmetric partners of a family of self-adjoint operators which are self-adjoint extensions of the differential operator
In this paper, we use soft linear operators to introduce the notion of discrete frames on soft Hilbert spaces, which extends the classical notion of frames on Hilbert spaces to the context of algebraic structures on soft sets. Among other results, we...
This study presents a gradient-based topology optimisation framework for heat sinks embedded with phase-change material (PCM) that targets the mitigation of temperature oscillations under cyclic thermal loads. The approach couples transient thermal d...
We study a separable Hilbert space of smooth curves taking values in the Segal–Bergmann space of analytic functions in the complex plane, and two of its subspaces that are the domains of unbounded non self-adjoint linear partial differential op...
Linearizations of the spherical harmonic discrete ordinate method (SHDOM) by means of a forward and a forward-adjoint approach are presented. Essentially, SHDOM is specialized for derivative calculations and radiative transfer problems involving the...
This paper presents a concurrent topology optimization of multi-scale composite structures subjected to general time-dependent loads for minimizing dynamic compliance. A three-field density-based method is adopted to implement the concurrent topologi...
To meet the stringent reliability requirements of rotor blades in turbomachines, greater effort should be devoted to improving both aerodynamic and structural performance in blade design. This paper introduces an aero-structural multi-disciplinary de...
A fractional wave equation with a fractional Riemann–Liouville derivative is considered. An arbitrary self-adjoint operator A with a discrete spectrum was taken as the elliptic part. We studied the inverse problem of determining the order of th...
We solve numerically a forest management optimization problem governed by a nonlinear partial differential equation (PDE), which is a size-structured population model. The formulated problem is supplemented with a natural constraint for a solution to...
The shielding calculation of neutron streaming problems with ducts is characterized by the strong anisotropy of angular flux, which poses a challenge for the analysis of nuclear installations. The discrete ordinate method is one of the most commonly...
The paper is devoted to the discrete Lyapunov equation
This article proposes a novel robust invariance condition for uncertain linear discrete-time systems with state and control constraints, utilizing a method of semidefinite programming duality. The approach involves approximating the robust invariant...
In order to merge continuous and discrete analyses, a number of dynamic derivative equations have been put out in the process of developing a time-scale calculus. The investigations that incorporated combined dynamic derivatives have led to the propo...
During this research, aerodynamic shape optimization is conducted on the Ahmed body with the drag coefficient as the objective function and the ramp shape as the design variable, while aero-structural optimization is conducted on NACA 0012 to reduce...
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...
In this paper, we study spectral properties of non-self-adjoint operators with the discrete spectrum. The main challenge is to represent a complete description of belonging to the Schatten class through the properties of the Hermitian real component....
Every aerodynamic optimization is proceeded by a parameterization of the studied aerial object, and due to its influence on the final optimization process, careful attention should be made in choosing the appropriate parameterization method. An aerod...
We investigate the self-adjoint extensions of the Dirac operator of a massive one-dimensional field of mass m confined in a finite filament of length L. We compute the spectrum of vacuum fluctuations of the Dirac field under the most general dispersi...
This study considers general Markov chains (MCs) with discrete time in an arbitrary phase space. The transition function of the MC generates two operators: T, which acts on the space of measurable functions, and A, which acts on the space of bounded...
This study presents the development of a discrete algorithm for interpreting ground-penetrating radar (GPR) data in vertically inhomogeneous media for the diagnostics of road structures. Experimental data were obtained using an OKO-2 GPR system, foll...
Communication systems based on chaotic synchronization are gaining interest in the area of secure and covert data transmission. In this paper, a novel digital communication technique based on a coherent chaotic data transmission approach is proposed....
This paper tackles the ill-posed inversion of initial conditions and diffusion coefficient for Burgers’ equation with a source term. Using optimal control theory combined with a finite difference discretization scheme and a dual-functional desc...
The adjoint thermodynamic and heat exchange processes in the new class piston compressor with regenerative heat exchange are considered in the paper. The implicit tridiagonal matrix algorithm is implemented to study the unsteady thermal conductivity...
We consider a general second order self-adjoint elliptic operator on an arbitrary metric graph, to which a small graph is glued. This small graph is obtained via rescaling a given fixed graph
We consider bounded continuous fields of self-adjoint operators which are parametrized by a locally compact Hausdorff space
In this research, we investigate an optimal control problem governed by elliptic PDEs with Dirichlet boundary conditions on complex connected domains, which can be utilized to model the cooling process of concrete dam pouring. A new convergence resul...
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