GitHub - nnagyd/CPU_ODE_solvers: Optimizing numerical ODE solvers using AVX instruction set on CPUs in C++

Discription

Optimizing numerical ODE solvers using AVX instruction set (with VCL library) on CPUs in C++
Using gcc compiler and linux perf profiler
CPU: Intel Core i7-4820K
- 3.8 GHz
- 30.4 double GFLOPS max
- Ivy Bridge microarchitecture

Basic test equation
- $x' = x^2-p \quad p \in [0.1;10] \quad N_p = 131072$
- Using RK4 solver with fix step
  - basic_test_RK4 folder
Division test equation
- $x' = \frac 1 x - p \cdot x \quad p \in [0;0.8] \quad N_p = 18144$
- Using RK4 solver with fix step
  - division_test_RK4 folder
Transcendental test equation
- $x' = p \cdot \sin(x) \quad p \in [0.1;1] \quad N_p = 18144$
- Using RK4 solver with fix step
  - transcendental_test_RK4 folder
Lorentz equation
- $x_1' = 10(x_2-x_1) \quad x_2' = p \cdot x_1 - x_2 - x_1 \cdot x_3 \quad x'_3 = x_1 \cdot x_2 - \frac 8 3 \cdot x_3$ ; $\quad p \in [0;21] \quad N_p = 40320$
- Using RK4 solver with fix step
  - lorentz_RK4 folder
- Using RKCK45 adaptive solver
  - lorentz_RKCK45 folder
Duffing equation
- $x_1' = x_2 \quad x_2' = x_1(1-x_1^2) - k \cdot x_2 + 0.3\cdot\cos(t) \quad k \in [0.2;0.3] \quad N_k = 46080$
- Using RKCK45 adaptive solver
  - duffing_RKCK45 folder

Program	Solver	RollOut	Runtime	Parameter number	GFLOPS	% of max	Special functions
Basic test	RK4	6	1.577 s	181440	24.7	81%	-
Division test	RK4	2	1.333 s	18144	3.4	11%	division in ODE
Transcendental test	RK4	4	3.143 s	18144	10.7	35%	sine in ODE
Lorentz	RK4	2	1.438 s	40320	21.3	70%	-
Lorentz	RKCK45	1	2.129 s	40320	10.8	36%	log,exp,division by stepsize prediction
Duffing	RKCK45	1	240 s	46080	10.6	35%	Cosine in ODE and log,exp,division by stepsize prediction

Name		Name	Last commit message	Last commit date
Latest commit History 70 Commits
basic_test_RK4		basic_test_RK4
division_test_RK4		division_test_RK4
duffing_RKCK45		duffing_RKCK45
lorentz_RK4		lorentz_RK4
lorentz_RKCK45		lorentz_RKCK45
transcendental_test_RK4		transcendental_test_RK4
README.md		README.md