Heat Conduction Using Greens Functions

Cole, Kevin D.; Beck, James V.; Haji-Sheikh, A.; Litkouhi, Bahman

doi:10.1201/9781439895214

Cited by 152 publications

(151 citation statements)

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“…where Q is the (effective) rate of energy supplied to the system, v is the velocity of the laser, and a, b, c are the main dimensions of the ellipsoid, as shown in Figure 7A. The problem at hand is linear and admits a semianalytical solution using Green's functions 63,64 given by…”

Section: Verification Of the Thermal Fe Modelmentioning

confidence: 99%

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

Neiva

Badia

Martı́n

et al. 2019

Numerical Meth Engineering

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Summary This work introduces an innovative parallel fully‐distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well known that virtual part design and qualification in additive manufacturing requires highly accurate multiscale and multiphysics analyses. Only high performance computing tools are able to handle such complexity in time frames compatible with time‐to‐market. However, efficiency, without loss of accuracy, has rarely held the centre stage in the numerical community. Here, in contrast, the framework is designed to adequately exploit the resources of high‐end distributed‐memory machines. It is grounded on three building blocks: (1) hierarchical adaptive mesh refinement with octree‐based meshes; (2) a parallel strategy to model the growth of the geometry; and (3) state‐of‐the‐art parallel iterative linear solvers. Computational experiments consider the heat transfer analysis at the part scale of the printing process by powder‐bed technologies. After verification against a three‐dimensional (3D) benchmark, a strong‐scaling analysis assesses performance and identifies major sources of parallel overhead. A third numerical example examines the efficiency and robustness of (2) in a curved 3D shape. Unprecedented parallelism and scalability were achieved in this work. Hence, this framework contributes to take on higher complexity and/or accuracy, not only of part‐scale simulations of metal or polymer additive manufacturing but also in welding, sedimentation, atherosclerosis, or any other physical problem where the physical domain of interest grows in time.

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Section: Verification Of the Thermal Fe Modelmentioning

confidence: 99%

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

Neiva

Badia

Martı́n

et al. 2019

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…where C ρϕ (ρ, ϕ, t|ρ tx , ϕ tx , t 0 ) and C z (z, t|z tx , t 0 ) are radial-azimuthal and axial direction Green's functions. Thereby, (5) reduces to the following two independent equations [37]:…”

Section: Cgf Of Diffusion In Biological Cylindrical Environmentmentioning

confidence: 99%

“…Equation (16) is Bessel's equation with general solution [37] R n (ρ|ρ tx ) = A n J n (λ n ρ) + B n Y n (λ n ρ),…”

Section: A Derivation Of Radial-azimuthal Cgfmentioning

confidence: 99%

Diffusive Molecular Communication in Biological Cylindrical Environment

Zoofaghari

Arjmandi

2019

IEEE Trans.on Nanobioscience

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Diffusive molecular communication (DMC) is one of the most promising approaches for realizing nano-scale communications in biological environments for healthcare applications. In this paper, a DMC system in biological cylindrical environment is considered, inspired by blood vessel structures in the body. The internal surface of the cylinder boundary is assumed to be covered by the biological receptors which may irreversibly react with hitting molecules. Also, information molecules diffusing in the fluid medium are subject to a degradation reaction and flow. The concentration Green's function of diffusion in this environment is analytically derived which takes into account asymmetry in all radial, axial and azimuthal coordinates. Employing obtained Green's function, information channel between transmitter and transparent receiver of DMC is characterized. To evaluate the DMC system in the biological cylinder, a simple on-off keying modulation scheme is adopted and corresponding error probability is derived.Particle based simulation results confirm the proposed analysis. Also, the effect of different system parameters on the concentration Green's function are examined. Our results reveal that the degradation reaction and the boundary covered by biological receptors may be utilized to mitigate intersymbol interference and outperform corresponding error probability. Index TermsDiffusive molecular communication (DMC), biological environment, partial differential equation, Green's function.

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“…By considering this initial condition and removing the source term in (4), we obtain a homogeneous PDE that can be solved by the well-known technique of separation of variables [27]. The solution with separated variables is considered as follows:…”

Section: A Cgf Of Diffusion In Biological Spherical Environmentmentioning

confidence: 99%

Diffusive Molecular Communication in a Biological Spherical Environment With Partially Absorbing Boundary

Arjmandi

Zoofaghari

Noel

2019

IEEE Trans. Commun.

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Diffusive molecular communication (DMC) is envisioned as a promising approach to help realize healthcare applications within bounded biological environments. In this paper, a DMC system within a biological spherical environment (BSE) is considered, inspired by bounded biological sphere-like structures throughout the body. As a biological environment, it is assumed that the inner surface of the sphere's boundary is fully covered by biological receptors that may irreversibly react with hitting molecules. Moreover, information molecules diffusing in the sphere may undergo a degradation reaction and be transformed to another molecule type. Concentration Green's function (CGF) of diffusion inside this environment is analytically obtained in terms of a convergent infinite series. By employing the obtained CGF, the information channel between transmitter and transparent receiver of DMC in this environment is characterized. Interestingly, it is revealed that the information channel is reciprocal, i.e., interchanging the position of receiver and transmitter does not change the information channel. Results indicate that the conventional simplifying assumption that the environment is unbounded may lead to an inaccurate characterization in such biological environments. Index TermsDiffusive molecular communication (DMC), bounded biological environment, Green's function, Error probability.

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Heat Conduction Using Greens Functions

Cited by 152 publications

References 0 publications

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

Diffusive Molecular Communication in Biological Cylindrical Environment

Diffusive Molecular Communication in a Biological Spherical Environment With Partially Absorbing Boundary

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