Algorithms and Data Structures for Multi-Adaptive Time-Stepping

• Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the multi-adaptive methods allow individual and adaptive time steps to be used for different components or in different regions of space. We present algorithms for efficient multi-adaptive time-stepping, including the recursive construction of time slabs and adaptive time step selection. We also present data structures for efficient storage and interpolation of the multi-adaptive solution. The efficiency of the proposed algorithms and data structures is demonstrated for a series of benchmark problems.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

Algorithms

Performance

Multi-adaptivity

individual time steps

local

time steps

multirate

ODE

continuous Galerkin

discontinuous

Galerkin

mcgq

mdgq

C plus

implementation

algorithms

DOLFIN

ordinary differential-equations

finite-element methods

locally

varying time

parabolic problems

galerkin methods

conservation-laws

approximations

integration

schemes

model

Algorithms

C+

Continuous Galerkin

Discontinuous Galerkin

DOLFIN

Implementation

Individual time steps

Local time steps

Mcgq

Mdgq

Multi-adaptivity

Multirate

ODE

Publication and Content Type

ref (subject category)

art (subject category)