4 papers
Convergence rates of curved boundary element methods for the 3D Laplace and Helmholtz equations
Luiz Maltez Faria, Pierre Marchand, Hadrien Montanelli
We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our…
Equation level matching: An extension of the method of matched asymptotic expansion for problems of wave propagation
Luiz M. Faria, Rodolfo R. Rosales
We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions…
Study of a model equation in detonation theory: multidimensional effects
Luiz M. Faria, Aslan R. Kasimov, Rodolfo R. Rosales
We extend the reactive Burgers equation presented in Kasimov et al. Phys. Rev. Lett., 110 (2013) and Faria et al. SIAM J. Appl. Maths, 74 (2014), to include multidimensional effect…
Set-valued solutions for non-ideal detonation
Roman Semenko, Luiz Faria, Aslan Kasimov +1
The existence and structure of steady gaseous detonation propagating in a packed bed of solid inert particles are analyzed in the one-dimensional approximation by taking into consi…