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- Creator:
- Djellouli, Rabia, Gillman, Adrianna, and Amara, Mohamed
- Description:
- A mixed-hybrid-type formulation is proposed for solving Helmholtz problems. This method is based on (a) a local approximation of the solution by oscillated finite element polynomials and (b) the use of Lagrange multipliers to “weakly” enforce the continuity across element boundaries. The computational complexity of the proposed discretization method is determined mainly by the total number of Lagrange multiplier degrees of freedom introduced at the interior edges of the finite element mesh, and the sparsity pattern of the corresponding system matrix. Preliminary numerical results are reported to illustrate the potential of the proposed solution methodology for solving efficiently Helmholtz problems in the mid- and high-frequency regimes.
- Resource Type:
- Article
- Identifier:
- 0377-0427
- Campus Tesim:
- Northridge
- Creator:
- Sethuraman, Bharath and Košir, Tomaž
- Description:
- We study components and dimensions of higher-order determinantal varieties obtained by considering generic m×n (m⩽n) matrices over rings of the form F[t]/(tk), and for some fixed r, setting the coefficients of powers of t of all r×r minors to zero. These varieties can be interpreted as spaces of (k−1)th order jets over the classical determinantal varieties; a special case of these varieties first appeared in a problem in commuting matrices. We show that when r=m, the varieties are irreducible, but when r<m, these varieties are reducible. We show that when r=2<m (any k), there are exactly ⌊k/2⌋+1 components, which we determine explicitly, and for general r<m, we show there are at least ⌊k/2⌋+1 components. We also determine the components explicitly for k=2 and 3 for all values of r (for k=3 for all but finitely many pairs of (m,n)).
- Resource Type:
- Article
- Identifier:
- 0022-4049
- Campus Tesim:
- Northridge
- Creator:
- Saint-Guirons, Anne-Gaelle, Djellouli, R., and Barucq, Helene
- Description:
- We propose a new class of approximate local DtN boundary conditions to be applied on prolate spheroidal-shaped exterior boundaries when solving problems of acoustic scattering by elongated obstacles. These conditions are: (a) exact for the first modes, (b) easy to implement and to parallelize, (c) compatible with the local structure of the computational finite element scheme, and (d) applicable to exterior ellipsoidal-shaped boundaries that are more suitable in terms of cost-effectiveness for surrounding elongated scatterers. We investigate analytically and numerically the effect of the frequency regime and the slenderness of the boundary on the accuracy of these conditions. We also compare their performance to the second-order absorbing boundary condition (BGT2) designed by Bayliss, Gunzburger and Turkel when expressed in prolate spheroid coordinates. The analysis reveals that, in the low-frequency regime, the new second-order DtN condition (DtN2) retains a good level of accuracy regardless of the slenderness of the boundary. In addition, the DtN2 boundary condition outperforms the BGT2 condition. Such superiority is clearly noticeable for large eccentricity values.
- Resource Type:
- Article
- Identifier:
- 0377-0427
- Campus Tesim:
- Northridge
- Creator:
- Jonov, Boyan
- Description:
- We show in this paper that the principal component of the first-order jet scheme over the classical determinantal variety of m×n matrices of rank at most 1 is arithmetically Cohen–Macaulay, by showing that an associated Stanley–Reisner simplicial complex is shellable.
- Resource Type:
- Article
- Identifier:
- 0022-4049
- Campus Tesim:
- Northridge
- Creator:
- Reiner, Robert C., Harari, Isaac, and Djellouli, Rabia
- Description:
- A mathematical and numerical analysis is performed to assess the performance of the second order Bayliss–Gunzburger–Turkel (BGT2) condition when applied to solving low-frequency acoustic scattering problems in the case of elongated scatterers. This investigation suggests that BGT2 retains an acceptable level of accuracy for relatively low wavenumber. A damping effect is incorporated to the BGT2 condition in order to extend the range of satisfactory performance. This damping procedure consists in adding only a constant imaginary part to the wavenumber. The numerical results indicate that the modified version of BGT2 extends the range of satisfactory performance by improving the level of accuracy by up to two orders of magnitude. Guidelines on the appropriate choice of the damping coefficient are provided.
- Resource Type:
- Article
- Identifier:
- 0377-0427
- Campus Tesim:
- Northridge
- Creator:
- Ghoniem, Nasr M., Chen, Zhengzheng, Takahashi, Akiyuki, and Kioussis, Nicholas G.
- Description:
- Oxide dispersion strengthened (ODS) steels are promising candidates for applications in fusion and fission rectors. Y2O3 particles dispersed in an iron matrix drastically improve the strength without adverse effects on ductility. We investigate here details of the dislocation core structure in Y2O3 precipitates, and at the interface between the iron matrix and the Y2O3 precipitate. We also simulate dislocation interaction with nano-size Y2O3 precipitates. It is shown that the γ-surface energies on planes between oxygen atoms and metallic atoms are extremely high, and that dislocations in an iron matrix cannot penetrate into Y2O3 particles. Three-dimensional parametric dislocation dynamics simulations of the interaction between an edge dislocation and an Y2O3 particle are carried out. The results show that the critical resolved shear stress (CRSS) has a strong dependence on the lattice mismatch Y2O3 particles and the iron matrix, and that it is lower than analytically calculated values of the Orowan stress.
- Resource Type:
- Article
- Identifier:
- 0022-3115
- Campus Tesim:
- Northridge
- Creator:
- Saint-Guirons, Anne-Gaelle, Djellouli, R., and Barucq, Helene
- Description:
- We propose a new class of approximate local DtN boundary conditions to be applied on prolate spheroidal-shaped exterior boundaries when solving problems of acoustic scattering by elongated obstacles. These conditions are: (a) exact for the first modes, (b) easy to implement and to parallelize, (c) compatible with the local structure of the computational finite element scheme, and (d) applicable to exterior ellipsoidal-shaped boundaries that are more suitable in terms of cost-effectiveness for surrounding elongated scatterers. We investigate analytically and numerically the effect of the frequency regime and the slenderness of the boundary on the accuracy of these conditions. We also compare their performance to the second-order absorbing boundary condition (BGT2) designed by Bayliss, Gunzburger and Turkel when expressed in prolate spheroid coordinates. The analysis reveals that, in the low-frequency regime, the new second-order DtN condition (DtN2) retains a good level of accuracy regardless of the slenderness of the boundary. In addition, the DtN2 boundary condition outperforms the BGT2 condition. Such superiority is clearly noticeable for large eccentricity values.
- Resource Type:
- Article
- Identifier:
- 0377-0427
- Campus Tesim:
- Northridge
- Creator:
- Freeman, Arthur J. and Wu, Ruqian
- Description:
- First-principles electronic structure studies based on local spin density functional theory and performed on extremely complex simulations of ever increasingly realistic systems, play a very important role in explaining and predicting surface and interface magnetism. This review deals with what is a major issue for first-principles theory, namely the theoretical/computational treatment of the weak spin-orbit coupling in magnetic transition metals and their alloys and its important physical consequences: magneto-crystalline anisotropy, magnetostriction, magneto-optical Kerr effects and X-ray magnetic circular dichroism. As is demonstrated, extensive first-principles calculations and model analyses now provide simple physical insights and guidelines to search for new magnetic recording and sensor materials.
- Resource Type:
- Article
- Identifier:
- 0304-8853
- Campus Tesim:
- Northridge
- Creator:
- Amara, Mohamed, Gillman, Adrianna, and Djellouli, Rabia
- Description:
- A mixed-hybrid-type formulation is proposed for solving Helmholtz problems. This method is based on (a) a local approximation of the solution by oscillated finite element polynomials and (b) the use of Lagrange multipliers to “weakly” enforce the continuity across element boundaries. The computational complexity of the proposed discretization method is determined mainly by the total number of Lagrange multiplier degrees of freedom introduced at the interior edges of the finite element mesh, and the sparsity pattern of the corresponding system matrix. Preliminary numerical results are reported to illustrate the potential of the proposed solution methodology for solving efficiently Helmholtz problems in the mid- and high-frequency regimes.
- Resource Type:
- Article
- Identifier:
- 0377-0427
- Campus Tesim:
- Northridge
- Creator:
- Reiner, Robert C., Harari, Isaac, and Djellouli, Rabia
- Description:
- A mathematical and numerical analysis is performed to assess the performance of the second order Bayliss–Gunzburger–Turkel (BGT2) condition when applied to solving low-frequency acoustic scattering problems in the case of elongated scatterers. This investigation suggests that BGT2 retains an acceptable level of accuracy for relatively low wavenumber. A damping effect is incorporated to the BGT2 condition in order to extend the range of satisfactory performance. This damping procedure consists in adding only a constant imaginary part to the wavenumber. The numerical results indicate that the modified version of BGT2 extends the range of satisfactory performance by improving the level of accuracy by up to two orders of magnitude. Guidelines on the appropriate choice of the damping coefficient are provided.
- Resource Type:
- Article
- Identifier:
- 0377-0427
- Campus Tesim:
- Northridge