A Time—Adaptive Semi—Lagrangian Approximation to Mean Curvature Motion

Polycrystalline materials typically contain a very large number of grains whose surrounding grain boundaries evolve over time to reducethe overall energy of the microstructure. The evolution of the microstructure is influencedby the motion of the exterior surface since the grain boundaries couple to the exterior surface of the specimen; these effects can be appreciable especially in thin specimens. We model these effects using the classical framework of Mullins, in whichgrain boundaries move by mean curvature motion, Vn =A κ, and the exterior surface evolves by surface diffusion, Vn = -BΔs κ. Here Vn and κ denote the normal velocity and the mean curvature of the respective evolving surfaces, and Δs is the surface Laplacian. A classical way to determine A, the ``reduced mobility," is to make measurements based on the half-loop bicrystalline geometry. In this geometry one of the two grains, which embedded within the other, recedes at a roughly constant rate which can provide an estimate for A. In this note, we report on findings concerning the effects of the exterior surface on grain boundary motion and mobility measurements in the context of the half-loop bicrystalline geometry. We assume that the ratio of grain boundary energy to the exterior surface energy is small, and suitable assumptions are made of the specimen aspect ratio.

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Active Contours Based on Chambolle's Mean Curvature Motion

2007 IEEE International Conference on Image Processing ◽

10.1109/icip.2007.4378884 ◽

2007 ◽

Cited By ~ 11

Author(s):

Xavier Bresson ◽

Tony F. Chan

Keyword(s):

Mean Curvature ◽

Active Contours ◽

Mean Curvature Motion ◽

Curvature Motion

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An algorithm for Mean Curvature Motion

Interfaces and Free Boundaries ◽

10.4171/ifb/97 ◽

2004 ◽

pp. 195-218 ◽

Cited By ~ 62

Author(s):

Antonin Chambolle

Keyword(s):

Mean Curvature ◽

Mean Curvature Motion ◽

Curvature Motion

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A Representation Formula for the Mean Curvature Motion

SIAM Journal on Mathematical Analysis ◽

10.1137/s0036141000380334 ◽

2001 ◽

Vol 33 (4) ◽

pp. 827-846 ◽

Cited By ~ 17

Author(s):

R. Buckdahn ◽

P. Cardaliaguet ◽

M. Quincampoix

Keyword(s):

Mean Curvature ◽

Representation Formula ◽

Mean Curvature Motion ◽

Curvature Motion ◽

The Mean

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Kinerja OpenMP pada Pengolahan Citra dengan Model Curvature Motion

Indonesian Journal on Computing (Indo-JC) ◽

10.21108/indojc.2018.3.1.218 ◽

2018 ◽

Vol 3 (1) ◽

pp. 97

Author(s):

Hasbi Rabbani ◽

Putu Harry Gunawan

Keyword(s):

Finite Difference ◽

Mean Curvature ◽

Mean Curvature Motion ◽

Curvature Motion

Evolusi dari sebuah bentuk geometri meliputi perubahan curvature yang terdapat dalam bentuk tersebut. Perubahan curvature ini tidak lepas dari perpindahan titik-titik pembentuknya dan diformulakan sebagai Mean Curvature Motion (MCM). MCM telah dipelajari secara mendalam untuk menyelesaikan salah satunya kurva Jordan pada pemodelan fisis. Pada jurnal ini, solusi MCM diaproksimasi menggunakan skema finite difference dan disimulasikan ke dalam paralel OpenMP. Untuk menghitung performansi paralel, dilakukan simulasi sebanyak 10 niter berbeda pada thread sejumlah 2, 4, dan 8. Dari simulasi yang telah dilakukan, didapatkan hasil bahwa performa paralel lebih membutuhkan waktu komputasi yang lebih rendah daripada serial. Selain itu, didapat pula rata-rata efisiensi kode paralel menggunakan 2 Thread lebih tinggi daripada menggunakan 4 Thread dan 8 Thread. Sebagai contoh pada ukuran niter 50000, kecepatan masing-masing 2, 4, dan 8 Thread adalah 180.422, 156.002, dan 333.243 s, serta efisiensi masing-masing 2, 4, dan 8 Thread adalah 113%, 66%, dan 34,8%.

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