This volume contains 36 research papers written by prominent researchers. The papers are based on a large satellite conference on scientific computing held at the International Congress of Mathematics (ICM) in Xi'an, China. Topics covered include a variety of subjects in modern scientific computing and its applications, such as numerical discretization methods, linear solvers, parallel computing, high performance computing, and applications to solid and fluid mechanics, energy, environment, and semiconductors. The book will serve as an excellent reference work for graduate students and researchers working with scientific computing for problems in science and engineering.

Preface	p. ix
A scheme for compressible two-phase flows and interface problems	p. 1
Multi-level fast multipole Galerkin method for the boundary integral solution of the exterior Helmholtz equation	p. 13
An overview of subgrid upscaling for elliptic problems in mixed form	p. 21
Mixed finite elements for elasticity in the stress-displacement formulation	p. 33
New variants of defect correction for boundary value problems in ordinary differential equations	p. 43
Scientific computing in energy and environment	p. 51
Approximate analysis of extended Williamson fluids for Powell-Sabin-Heindl elements	p. 59
Frequency domain method for the scalar wave equation with second order absorbing boundary condition	p. 67
Scalable FETI with optimal dual penalty for semicoercive variational inequalities	p. 79
Algebraic multigrid and Schur complement strategies within a multilayer spectral element ocean model	p. 89
An improved alternating-direction method for a viscous wave equation	p. 99
Diverse vortex dynamics in superfluids	p. 105
Adaptive wavelet methods for advection-reaction equations	p. 119
Approximation of an MHD problem using Lagrange finite elements	p. 131
Best approximation for the p-version of the finite element method in three dimensions in the framework of the Jacobi-weighted Besov spaces	p. 139
Non-isotropic Jacobi spectral method	p. 157
Improved method for solving the heat equation with BEM and collocation	p. 165
Modelling of transport with non-equilibrium effects in dual-porosity media	p. 175
Error estimate for a two-level scheme of Newton type for the Navier-Stokes equations	p. 183
Mathematical modeling and numerical algorithms for poroelastic problems	p. 191
Fast Poisson solver in a three-dimensional ellipsoid	p. 203
Modeling horizontal wells with the CVFA method in black oil reservoir simulations	p. 209
Radial basis function based meshless method for groundwater modeling	p. 237
Upwinding finite covolume methods for unsteady convection-diffusion problems	p. 245
Parallel computing in the black oil model	p. 253
Finite element model of piezoelectric resonator	p. 263
Discontinuous finite element methods for acoustic and elastic wave problems	p. 271
Heuristics for developing variations on future air traffic schedule characteristics for air traffic simulation	p. 283
FEM/FVM modelling of processes in a combustion engine	p. 291
A finite control volume method for the reduction of an iron ore-coal composite pellet in an axisymmetric temperature field	p. 299
The fast multipole method for arbitrary Green's functions	p. 307
A mathematical model for ESP simulation	p. 315
Mixed-hybrid discrete fracture network model	p. 325
A new numerical algorithm for treatment of convective terms and its applications to PDEs	p. 333
Direct numerical simulation of turbulent channel flow with bubbles	p. 347
RKDG finite element schemes combined with a gas-kinetic method for one-dimensional compressible Euler equations	p. 355
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