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Quasicrystals are one kind of space-filling structures. The traditional crystalline approximant method utilizes periodic structures to approximate quasicrystals. The errors of this approach come from two parts: the numerical discretization, and the approximate error of Simultaneous Diophantine Approximation which also determines the size of the domain necessary for accurate solution. As the app...

where σ is the stress tensor, ǫ = 12 (∇u +∇u) T is the strain tensor, f is a body force per unit mass (gravity is a typical example), qT is a volume source (it may model chemical reactions, Joule effects, radioactive decay, etc.), and jT is the heat flux. In addition to the above three fundamental conservation equations, one may also have to add L equations that accounts for the conservation of...

Among the efficient numerical methods based on atomistic models, the quasicontinuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to multilattices (Tadmor et al, 1999). Another existing numerical approach to modeling multilattices is homogenization. In the present paper we revie...

The paper deals with numerical methods using defects The defects are used to sm(x~th numerical SOhltions, to construct a postericwi error estimates and difference schenles, to correct ~hltit)ns.

In the last years, numerical simulation has seen a great development thanks to costs reduction and speed increases of the computational systems. With these improvements, the mathematical algorithms are able to work properly with more realistic problems. Nowadays, the solution of a problem using numerical simulation is not just finding a result, but also to ensure the quality. However, can we sa...

We present a Jacobi-like algorithm for simultaneous diagonalization of commuting pairs of complex normal matrices by unitary similarity transformations. The algorithm uses a sequence of similarity transformations by elementary complex rotations to drive the oo-diagonal entries to zero. We show that its asymptotic convergence rate is quadratic and that it is numerically stable. It preserves the ...

Numerical methods are needed for derivatives pricing in cases where analytic solutions are either unavailable or not easily computable. Examples of the former case include American-style options and most discretely observed path-dependent options. Examples of the latter type include the analytic formula for valuing continuously observed Asian options in [28], which is very hard to calculate for...

We review some numerical methods for selfadjoint and nonselfadjoint boundary eigenvalue problems.