Harmonic extension from the exterior of a cylinder

2020 ◽  
pp. 1
Author(s):  
Stephen J. Gardiner ◽  
Hermann Render
Keyword(s):  
Harmonic Extension

scholarly journals Mesh moving techniques in fluid-structure interaction: robustness, accumulated distortion and computational efficiency

2020 ◽  
Author(s):  
Alexander Shamanskiy ◽  
Bernd Simeon
Keyword(s):  
Fluid Structure Interaction ◽  
Continuation Methods ◽  
Moving Mesh Method ◽  
Important Ingredient ◽  
Fluid Structure ◽  
Harmonic Extension ◽  
Structure Interaction ◽  
Computational Mesh ◽  
Mesh Method ◽  
Moving Fluid

AbstractAn important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh moving technique (MMT) used to adapt the computational mesh in the moving fluid domain. An ideal MMT is computationally inexpensive, can handle large mesh motions without inverting mesh elements and can sustain an FSI simulation for extensive periods of time without irreversibly distorting the mesh. Here we compare several commonly used MMTs which are based on the solution of elliptic partial differential equations, including harmonic extension, bi-harmonic extension and techniques based on the equations of linear elasticity. Moreover, we propose a novel MMT which utilizes ideas from continuation methods to efficiently solve the equations of nonlinear elasticity and proves to be robust even when the mesh undergoes extreme motions. In addition to that, we study how each MMT behaves when combined with the mesh-Jacobian-based stiffening. Finally, we evaluate the performance of different MMTs on a popular two-dimensional FSI benchmark reproduced by using an isogeometric partitioned solver with strong coupling.

Sets of determination and kernels of certain associated operators

2010 ◽  
Vol 53 (2) ◽  
pp. 503-510
Author(s):  
Arne Stray
Keyword(s):  
Unit Circle ◽  
Unit Disc ◽  
Closed Subset ◽  
Bounded Function ◽  
Harmonic Extension ◽  
Linear Map ◽  
Associated Operators

AbstractLet m be a measure supported on a relatively closed subset X of the unit disc. If f is a bounded function on the unit circle, let fm denote the restriction to X of the harmonic extension of f to the unit disc. We characterize those m such that the pre-adjoint of the linear map f → fm has a non-trivial kernel.

Harmonic Extension On An LB-Fractal

2015 ◽  
Vol 8 (9) ◽  
pp. 89-94
Author(s):  
Bhagwati Prasad ◽  
Kunti Mishra
Keyword(s):  
Harmonic Extension
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