GSS_spd for million unknowns  
        ---  fast   stable   parallelism  ---        

MAIL: gsp@grusoft.com
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GSS_spd is a novel sparse solver for symmetric positive definite matrices (SPD in abbreviation).
GSS_spd is about 20% faster than PARDISO in numerical factorization. The result is based on nearly
all the large SPD matrices (with more than 300,000 unknowns) from UF sparse matrix collection,
which are indisputably authoritative and representative.
The testing CPU is Intel Q8200, which is cheap now. And the average numerical factorization time is less than 10 seconds!
So it’s easy and fast to solve million SPD matrices in PC.

GSS_spd 3.0 is available for commercial users.
GSS_spd 3.0 needs much less memory than 2.2.
GSS_spd 3.0 is faster than 2.2.

For more details, please contact

Phone: (+86) 013501997193
MAIL: gsp@grusoft.com
QQ: 304718494

Experimental Results

Table 1 lists the comparative testing between GSS_spd 2.2 and PARDISO in MKL 11.
The “numeric” column lists the time of numerical factorization.(in seconds)
The “solve” column lists the time of solve and iterative refinement. (in seconds)
The “err” column lists the forward err.
The “GSS_spd/PARDISO” column lists the ratio of numerical factorization time. As you see, GSS_spd is 20% faster than PARDISO in numerical factorization.
The testing CPU is INTEL Q8200 with 8G memory. The operating system is Windows Vista 64. Both GSS_spd and PARDISO use default parameters.

Table 1 comparative testing between GSS_spd and PARDISO

matrix

dimension

GSS_spd

PARDISO

GSS_spd/PARDISO

numeric

solve

err

numeric

solve

err

F1

343791

13.77

0.77

5.1e-11

16.44

2.43

5.8e-11

0.84

msdoor

415863

1.64

0.3

1.4e-8

1.75

1.78

2.1e-8

0.94

af_5_k101

503625

3.99

0.5

9.1e-9

4.66

1.56

2.4e-8

0.86

inline_1

503712

10.34

0.81

2.1e-8

11.75

2.48

1.4e-8

0.88

af_shell8

504855

3.45

0.5

4.1e-9

3.93

1.48

3.2e-9

0.88

parabolic_fem

525825

0.87

0.31

7.9e-10

1.15

0.58

2.3e-9

0.76

apache2

715176

12.7

0.9

2.1e-8

17.97

2.18

8.6e-10

0.71

tmt_sym

726713

1.03

0.44

1.4e-6

1.49

0.66

8.4e-7

0.69

boneS10

914898

17.2

1.33

1.8e-7

20.98

3.95

2.1e-7

0.82

audikw_1

943695

-

-

-

-

-

-

 

ldoor

952203

5.45

0.75

2.4e-10

6.39

2.39

2.4e-10

0.85

bone010

986703

-

-

-

-

-

-

 

ecology2

999999

1.59

0.66

1.2e-6

2.15

0.78

2.3e-9

0.74

thermal2

1228045

1.79

0.75

1.8e-10

2.47

1.19

7.0e-11

0.72

G3_circuit

1585478

4.41

1.19

3.8e-9

6.25

1.75

2.1e-10

0.71

sum

 

78.23

 

 

97.38

 

 

0.80

For detail, please see "GSS_spd quick start user guide.pdf"

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