Numerical Viscosity and Convergence of Finite Volume Methods for Conservation Laws with Boundary Conditions

1995 ◽  
Vol 32 (3) ◽  
pp. 775-796 ◽  
Author(s):  
S. Benharbit ◽  
A. Chalabi ◽  
J. P. Vila
Keyword(s):  
Boundary Conditions ◽  
Conservation Laws ◽  
Finite Volume ◽  
Finite Volume Methods ◽  
Numerical Viscosity

scholarly journals An error estimate for finite volume methods for multidimensional conservation laws

1994 ◽  
Vol 63 (207) ◽  
pp. 77-77 ◽  
Author(s):  
Bernardo Cockburn ◽  
Fr{éd{éric Coquel ◽  
Philippe LeFloch
Keyword(s):  
Error Estimate ◽  
Conservation Laws ◽  
Finite Volume ◽  
Finite Volume Methods

On the arithmetic intensity of high-order finite-volume discretizations for hyperbolic systems of conservation laws

2017 ◽  
Vol 33 (1) ◽  
pp. 25-52 ◽  
Author(s):  
J Loffeld ◽  
JAF Hittinger
Keyword(s):  
Conservation Laws ◽  
Finite Volume ◽  
Hyperbolic Systems ◽  
Finite Volume Methods ◽  
High Order ◽  
Floating Point ◽  
Systems Of Conservation Laws ◽  
Data Transfers ◽  
Blue Gene ◽  
Theory And Experiments

It has been conjectured that higher-order discretizations for partial differential equations will have advantages over the lower-order counterparts commonly used today. The reasoning is that the increase in arithmetic operations will be more than offset by the reduction in data transfers and the increase in concurrent floating-point units. To evaluate this conjecture, the arithmetic intensity of a class of high-order finite-volume discretizations for hyperbolic systems of conservation laws is theoretically analyzed for spatial discretizations from orders three through eight in arbitrary dimensions. Three cache models are considered: the limiting cases of no cache and infinite cache as well as a finite-sized cache model. Models are validated experimentally by measuring floating-point operations and data transfers on an IBM Blue Gene/Q node. Theory and experiments demonstrate that high-order finite-volume methods will be able to provide increases in arithmetic intensity that will be necessary to make better utilization of on-node floating-point capability.

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