Meshes

March 15, 2026

All meshes were generated using gmsh and can be downloaded here: meshes.tar.bz2.

Each mesh set contains 15 meshes with logarithmically spaced characteristic lengths from coarse to fine. Plain meshes contain only the magnetic body. Shell meshes add a “space” region (free space around the body) and a “transform” region (coordinate-transformed shell mapping to infinity).

Sphere#

Unit sphere (radius 0.5) centered at the origin.

Geometry: Radius: 0.5
Extent: [-0.49, 0.49] × [-0.50, 0.50] × [-0.50, 0.50]

Sphere

Mesh	Nodes	Tetrahedra
1	258	898
2	388	1,433
3	469	1,816
4	775	3,248
5	1,021	4,426
6	1,487	6,693
7	2,100	9,837
8	3,134	15,214
9	4,832	24,319
10	7,035	36,366
11	10,430	55,193
12	15,168	82,069
13	22,752	125,368
14	35,418	198,771
15	51,969	295,502

Sphere (spherical shell)#

Sphere embedded in two concentric spherical shells: space (r=1.0) and transform (r=3.0).

Geometry: Body radius: 0.5, space radius: 1.0, transform radius: 3.0
Extent: [-3.00, 2.99] × [-3.00, 2.99] × [-3.00, 3.00]

Sphere (spherical shell)

Mesh	Nodes	Total tets	body	transform	space
1	1,704	8,183	811	5,931	1,441
2	2,760	13,840	1,444	10,066	2,330
3	3,706	19,043	1,665	14,413	2,965
4	5,610	29,240	3,152	21,739	4,349
5	8,229	43,941	4,317	33,568	6,056
6	12,272	66,896	6,742	51,405	8,749
7	17,631	97,537	9,935	75,669	11,933
8	26,677	150,182	15,301	116,793	18,088
9	40,706	232,907	24,034	181,880	26,993
10	59,885	346,004	35,707	271,413	38,884
11	90,697	530,018	55,081	417,676	57,261
12	133,749	787,978	78,203	628,386	81,389
13	206,764	1,229,385	119,744	983,206	126,435
14	316,286	1,893,161	196,556	1,504,549	192,056
15	476,880	2,872,768	282,174	2,301,996	288,598

Sphere (parallelepiped shell)#

Sphere embedded in an inner box with 6 conforming frustums forming the shell.

Geometry: Body radius: 0.5, inner box: 1.0³, outer box: 3.0³
Extent: [-1.50, 1.50] × [-1.50, 1.50] × [-1.50, 1.50]

Sphere (parallelepiped shell)

Mesh	Nodes	Total tets	body	shell_+x	shell_-x	shell_+y	shell_-y	shell_+z	shell_-z	air
1	2,609	14,638	813	2,063	2,039	2,050	2,020	2,077	2,034	1,542
2	3,734	21,095	1,237	3,017	2,947	2,928	3,009	2,931	2,937	2,089
3	5,404	30,909	1,766	4,441	4,385	4,433	4,383	4,419	4,421	2,661
4	8,237	47,760	2,820	6,821	6,831	6,766	6,776	6,928	6,722	4,096
5	12,032	70,355	4,154	10,152	10,043	10,130	10,073	10,102	10,146	5,555
6	17,986	106,203	6,447	15,215	15,359	15,209	15,265	15,298	15,391	8,019
7	26,841	159,758	9,725	23,108	23,292	23,165	23,264	23,031	22,775	11,398
8	40,671	243,659	15,013	35,346	35,181	35,227	35,152	35,392	35,426	16,922
9	61,427	370,480	22,979	53,767	53,599	53,713	53,750	53,704	53,521	25,447
10	92,762	562,449	34,883	81,608	81,661	81,739	82,092	81,814	81,789	36,863
11	140,848	858,340	53,322	124,834	124,695	124,265	124,568	125,402	125,211	56,043
12	213,915	1,308,808	81,711	190,637	190,575	190,801	190,642	190,969	190,229	83,244
13	325,929	2,001,818	125,140	291,873	292,687	292,297	291,678	291,283	292,045	124,815
14	497,055	3,061,785	191,369	446,236	446,847	446,710	447,460	446,785	447,554	188,824
15	758,855	4,687,533	293,962	682,934	684,426	684,420	684,744	685,193	685,358	286,496

Cube#

Unit cube (side 1.0) centered at the origin.

Geometry: Side: 1.0
Extent: [-0.50, 0.50] × [-0.50, 0.50] × [-0.50, 0.50]

Cube

Mesh	Nodes	Tetrahedra
1	143	387
2	144	393
3	237	737
4	343	1,144
5	460	1,586
6	683	2,565
7	910	3,636
8	1,492	6,250
9	2,307	10,265
10	3,457	16,069
11	5,555	26,970
12	8,311	41,887
13	12,380	64,146
14	20,835	111,127
15	32,746	178,787

Cube (spherical shell)#

Cube embedded in two concentric spherical shells: space (r=1.0) and transform (r=3.0).

Geometry: Side: 1.0, space radius: 1.0, transform radius: 3.0
Extent: [-2.98, 2.98] × [-2.98, 2.98] × [-3.00, 3.00]

Cube (spherical shell)

Mesh	Nodes	Total tets	body	transform	space
1	554	2,414	378	1,544	492
2	819	3,679	726	2,229	724
3	1,266	5,952	1,115	3,651	1,186
4	1,767	8,639	1,581	5,240	1,818
5	2,652	13,267	2,430	8,332	2,505
6	3,674	18,919	3,468	12,181	3,270
7	5,625	29,593	4,656	20,230	4,707
8	8,688	47,021	7,965	31,753	7,303
9	13,007	71,697	12,564	48,521	10,612
10	19,306	107,890	18,970	74,169	14,751
11	30,350	173,018	31,580	117,706	23,732
12	45,713	263,839	48,659	180,502	34,678
13	68,751	400,416	71,954	280,336	48,126
14	104,505	615,008	110,890	431,741	72,377
15	164,171	975,450	178,515	685,313	111,622

Cube (parallelepiped shell)#

Cube embedded in an inner box with 6 conforming frustums forming the shell.

Geometry: Body: 1.0³, inner box: 2.0³, outer box: 6.0³
Extent: [-3.00, 3.00] × [-3.00, 3.00] × [-3.00, 3.00]

Cube (parallelepiped shell)

Mesh	Nodes	Total tets	body	shell_+x	shell_-x	shell_+y	shell_-y	shell_+z	shell_-z	space
1	797	3,638	386	432	430	437	431	439	429	654
2	1,027	4,702	369	616	617	607	609	617	617	650
3	1,829	8,773	738	1,104	1,090	1,099	1,076	1,083	1,083	1,500
4	2,329	11,357	1,116	1,404	1,384	1,399	1,371	1,399	1,373	1,911
5	3,506	17,600	1,591	2,181	2,171	2,225	2,233	2,186	2,218	2,795
6	5,554	28,318	2,565	3,515	3,671	3,619	3,627	3,679	3,593	4,049
7	7,365	37,997	3,443	5,004	4,951	5,028	5,024	4,965	5,009	4,573
8	12,698	67,536	6,165	8,796	8,776	8,548	8,797	8,821	8,854	8,779
9	18,448	100,449	10,262	13,013	12,945	12,893	12,906	13,024	12,696	12,710
10	28,454	156,684	16,063	20,476	20,338	20,520	20,550	20,441	20,448	17,848
11	44,971	252,978	27,009	32,647	32,714	32,494	32,748	32,705	32,588	30,073
12	69,951	399,107	41,579	52,216	52,347	51,902	52,383	51,960	52,158	44,562
13	109,027	630,150	63,822	83,441	83,470	83,480	83,197	83,410	83,238	66,092
14	177,287	1,036,838	110,926	135,797	136,291	135,780	135,782	136,019	135,449	110,794
15	285,631	1,689,043	178,387	221,320	221,203	221,135	220,944	221,713	221,699	182,642

Prolate cuboid#

Prolate cuboid (0.5 × 0.5 × 1.0) elongated along z, centered at the origin.

Geometry: Dimensions: 0.5 × 0.5 × 1.0
Extent: [-0.25, 0.25] × [-0.25, 0.25] × [-0.50, 0.50]

Prolate cuboid

Mesh	Nodes	Tetrahedra
1	203	582
2	249	757
3	351	1,124
4	506	1,747
5	619	2,265
6	849	3,266
7	1,261	5,158
8	1,957	8,335
9	2,803	12,609
10	4,039	18,783
11	6,038	29,161
12	8,475	42,160
13	12,326	63,325
14	18,583	97,687
15	26,623	143,050

Prolate cuboid (spherical shell)#

Prolate cuboid embedded in two concentric spherical shells.

Geometry: Body: 0.5 × 0.5 × 1.0, space radius: 1.0, transform radius: 3.0
Extent: [-3.00, 2.99] × [-2.99, 2.99] × [-3.00, 3.00]

Prolate cuboid (spherical shell)

Mesh	Nodes	Total tets	body	transform	space
1	1,658	7,898	582	5,904	1,412
2	2,591	12,798	711	10,104	1,983
3	3,634	18,522	1,129	14,479	2,914
4	5,292	27,383	1,750	21,598	4,035
5	7,713	40,892	2,231	33,301	5,360
6	11,636	63,001	3,240	51,669	8,092
7	16,681	91,887	4,977	75,668	11,242
8	25,787	144,631	8,342	117,798	18,491
9	38,537	219,209	12,623	179,860	26,726
10	57,156	329,108	18,783	272,208	38,117
11	86,606	504,114	29,266	416,889	57,959
12	127,973	752,303	41,911	628,789	81,603
13	196,084	1,162,736	63,408	970,714	128,614
14	302,287	1,805,805	97,582	1,511,303	196,920
15	452,921	2,722,630	142,103	2,300,940	279,587

Prolate cuboid (parallelepiped shell)#

Prolate cuboid embedded in an inner box with 6 conforming frustums.

Geometry: Body: 0.5 × 0.5 × 1.0, inner box: 1.0 × 1.0 × 2.0, outer box: 3.0 × 3.0 × 6.0
Extent: [-1.50, 1.50] × [-1.50, 1.50] × [-3.00, 3.00]

Prolate cuboid (parallelepiped shell)

Mesh	Nodes	Total tets	body	shell_+x	shell_-x	shell_+y	shell_-y	shell_+z	shell_-z	space
1	1,368	6,301	579	852	865	864	852	652	678	959
2	1,874	8,783	738	1,259	1,247	1,225	1,204	961	943	1,206
3	2,470	11,967	1,133	1,566	1,564	1,582	1,541	1,387	1,424	1,770
4	3,697	18,190	1,723	2,300	2,350	2,358	2,351	2,214	2,223	2,671
5	4,799	23,943	2,153	3,259	3,237	3,245	3,220	2,823	2,777	3,229
6	7,253	37,472	3,233	5,113	5,068	5,083	5,101	4,521	4,429	4,924
7	10,235	53,591	4,930	7,204	7,201	7,182	7,119	6,588	6,557	6,810
8	15,582	83,226	8,415	10,906	10,929	11,001	10,988	10,140	10,042	10,805
9	23,170	126,194	12,518	16,880	16,702	16,455	16,723	15,742	15,989	15,185
10	33,215	183,652	18,731	24,276	24,102	24,184	24,110	22,918	22,966	22,365
11	48,612	272,326	29,074	35,670	35,886	35,947	35,840	34,350	34,642	30,917
12	71,351	405,160	41,794	53,990	53,499	53,821	53,781	52,213	51,624	44,438
13	106,529	612,555	63,256	81,141	81,151	81,536	81,560	79,396	79,313	65,202
14	161,067	936,664	97,641	123,827	124,210	123,889	123,757	122,212	121,902	99,226
15	239,580	1,407,447	141,634	189,132	188,134	188,381	188,864	183,089	183,849	144,364

Oblate cuboid#

Oblate cuboid (1.0 × 1.0 × 0.5) flattened along z, centered at the origin.

Geometry: Dimensions: 1.0 × 1.0 × 0.5
Extent: [-0.50, 0.50] × [-0.50, 0.50] × [-0.25, 0.25]

Oblate cuboid

Mesh	Nodes	Tetrahedra
1	154	407
2	214	624
3	307	979
4	412	1,365
5	696	2,594
6	870	3,313
7	1,336	5,429
8	1,907	8,119
9	2,673	11,957
10	4,030	18,820
11	5,971	28,823
12	8,158	40,663
13	12,253	62,709
14	18,591	97,810
15	27,165	146,336

Oblate cuboid (spherical shell)#

Oblate cuboid embedded in two concentric spherical shells.

Geometry: Body: 1.0 × 1.0 × 0.5, space radius: 1.0, transform radius: 3.0
Extent: [-3.00, 3.00] × [-2.99, 3.00] × [-3.00, 3.00]

Oblate cuboid (spherical shell)

Mesh	Nodes	Total tets	body	transform	space
1	901	4,119	399	2,941	779
2	1,374	6,530	608	4,691	1,231
3	1,974	9,685	992	6,966	1,727
4	2,756	13,748	1,354	10,015	2,379
5	4,232	21,887	2,594	15,470	3,823
6	5,892	30,692	3,279	22,640	4,773
7	9,065	48,753	5,429	35,880	7,444
8	13,375	73,262	8,107	54,407	10,748
9	20,248	113,055	11,974	85,686	15,395
10	30,155	170,852	18,724	129,475	22,653
11	46,995	269,937	28,643	206,514	34,780
12	69,668	404,243	40,626	315,034	48,583
13	107,585	631,283	62,176	495,417	73,690
14	165,484	980,127	96,511	768,231	115,385
15	249,407	1,487,589	145,171	1,179,620	162,798

Oblate cuboid (parallelepiped shell)#

Oblate cuboid embedded in an inner box with 6 conforming frustums.

Geometry: Body: 1.0 × 1.0 × 0.5, inner box: 2.0 × 2.0 × 1.0, outer box: 6.0 × 6.0 × 3.0
Extent: [-3.00, 3.00] × [-3.00, 3.00] × [-1.50, 1.50]

Oblate cuboid (parallelepiped shell)

Mesh	Nodes	Total tets	body	shell_+x	shell_-x	shell_+y	shell_-y	shell_+z	shell_-z	space
1	1,115	5,078	399	564	559	550	557	789	808	852
2	1,555	7,157	617	828	817	833	818	1,104	1,103	1,037
3	2,263	10,725	954	1,274	1,257	1,285	1,248	1,586	1,605	1,516
4	3,278	16,036	1,361	1,919	1,985	1,963	1,854	2,315	2,332	2,307
5	5,206	26,338	2,591	3,111	3,106	3,142	3,139	3,664	3,672	3,913
6	6,779	34,253	3,214	4,168	4,286	4,228	4,253	4,893	4,849	4,362
7	10,300	53,941	5,419	6,690	6,591	6,535	6,693	7,438	7,343	7,232
8	14,825	78,925	8,065	9,864	9,775	9,657	9,704	10,965	10,772	10,123
9	20,813	112,852	12,064	14,172	14,194	14,273	14,196	15,211	15,444	13,298
10	32,455	178,839	18,722	22,739	22,617	22,793	22,564	24,307	24,280	20,817
11	47,788	267,737	28,504	34,243	34,327	34,047	34,109	36,389	36,065	30,053
12	71,549	406,507	40,620	52,436	52,279	52,622	52,292	56,075	56,166	44,017
13	106,389	611,063	62,243	79,324	79,525	78,907	79,242	83,714	83,389	64,719
14	160,635	934,135	96,668	122,422	122,427	121,938	121,803	126,649	126,895	95,333
15	244,118	1,433,756	145,265	188,391	188,307	188,804	188,465	195,129	195,118	144,277

Prolate ellipsoid#

Prolate spheroid (a=b=0.25, c=0.5) elongated along z.

Geometry: Semi-axes: a=b=0.25, c=0.5
Extent: [-0.25, 0.25] × [-0.25, 0.25] × [-0.50, 0.50]

Prolate ellipsoid

Mesh	Nodes	Tetrahedra
1	167	505
2	200	609
3	288	970
4	397	1,428
5	619	2,440
6	862	3,462
7	1,264	5,502
8	1,878	8,536
9	2,818	13,263
10	4,051	19,680
11	6,067	30,637
12	9,110	47,318
13	13,640	72,479
14	20,844	113,171
15	31,700	175,811

Prolate ellipsoid (spherical shell)#

Prolate spheroid embedded in two concentric spherical shells.

Geometry: Semi-axes: a=b=0.25, c=0.5, space radius: 1.0, transform radius: 3.0
Extent: [-3.00, 2.99] × [-3.00, 2.99] × [-3.00, 3.00]

Prolate ellipsoid (spherical shell)

Mesh	Nodes	Total tets	body	transform	space
1	2,891	14,188	505	11,855	1,828
2	4,379	22,326	598	18,973	2,755
3	6,302	32,750	977	28,089	3,684
4	9,209	49,096	1,418	42,335	5,343
5	13,971	75,710	2,348	65,299	8,063
6	21,772	120,636	3,645	104,361	12,630
7	32,124	181,181	5,391	157,637	18,153
8	49,784	284,111	8,373	248,201	27,537
9	74,897	433,433	13,066	378,311	42,056
10	116,372	681,241	19,100	597,977	64,164
11	177,822	1,050,566	29,281	925,243	96,042
12	274,888	1,636,623	44,509	1,444,659	147,455
13	419,708	2,518,164	68,914	2,225,341	223,909
14	656,698	3,966,177	106,494	3,504,348	355,335
15	1,010,027	6,132,261	165,864	5,421,428	544,969

Prolate ellipsoid (parallelepiped shell)#

Prolate spheroid embedded in an inner box with 6 conforming frustums.

Geometry: Semi-axes: a=b=0.25, c=0.5, inner box: 0.5 × 0.5 × 1.0, outer box: 1.5 × 1.5 × 3.0
Extent: [-0.75, 0.75] × [-0.75, 0.75] × [-1.50, 1.50]

Prolate ellipsoid (parallelepiped shell)

Mesh	Nodes	Total tets	body	shell_+x	shell_-x	shell_+y	shell_-y	shell_+z	shell_-z	air
1	697	3,177	636	365	324	336	333	290	293	600
2	780	3,596	631	457	416	401	413	288	298	692
3	1,051	4,836	922	595	563	571	566	391	406	822
4	1,560	7,512	1,461	885	869	854	866	726	694	1,157
5	2,352	11,645	2,619	1,324	1,262	1,296	1,311	1,017	1,040	1,776
6	2,966	14,889	3,635	1,588	1,579	1,564	1,565	1,415	1,425	2,118
7	4,582	23,542	6,086	2,488	2,337	2,373	2,408	2,326	2,328	3,196
8	6,175	32,092	8,719	3,464	3,248	3,242	3,277	2,953	2,958	4,231
9	9,176	49,032	12,740	5,363	5,110	5,142	5,169	4,759	4,829	5,920
10	13,302	72,244	21,222	7,559	7,142	7,141	7,133	6,761	6,738	8,548
11	20,236	111,687	31,814	11,705	11,168	11,265	11,127	11,286	11,388	11,934
12	29,089	162,400	44,791	17,615	16,864	16,791	16,749	16,586	16,768	16,236
13	43,464	246,467	69,164	26,725	25,591	25,556	25,407	25,261	25,852	22,911
14	64,734	371,021	107,570	40,501	38,285	38,359	38,387	37,749	37,679	32,491
15	99,871	580,282	171,308	62,009	59,095	59,392	59,226	60,749	60,287	48,216

Oblate ellipsoid#

Oblate spheroid (a=b=0.5, c=0.25) flattened along z.

Geometry: Semi-axes: a=b=0.5, c=0.25
Extent: [-0.49, 0.49] × [-0.49, 0.50] × [-0.25, 0.25]

Oblate ellipsoid

Mesh	Nodes	Tetrahedra
1	293	981
2	359	1,250
3	516	1,924
4	729	2,898
5	1,108	4,618
6	1,609	7,028
7	2,305	10,624
8	3,424	16,319
9	5,157	25,409
10	7,666	39,035
11	11,522	60,454
12	17,315	92,900
13	26,277	144,181
14	40,300	224,548
15	61,378	348,058

Oblate ellipsoid (spherical shell)#

Oblate spheroid embedded in two concentric spherical shells.

Geometry: Semi-axes: a=b=0.5, c=0.25, space radius: 1.0, transform radius: 3.0
Extent: [-3.00, 2.99] × [-3.00, 2.99] × [-3.00, 3.00]

Oblate ellipsoid (spherical shell)

Mesh	Nodes	Total tets	body	transform	space
1	3,053	15,197	1,000	11,855	2,342
2	4,561	23,424	1,218	18,973	3,233
3	6,579	34,430	1,860	28,089	4,481
4	9,564	51,250	2,623	42,303	6,324
5	14,503	78,992	4,337	65,336	9,319
6	22,541	125,377	6,827	104,371	14,179
7	33,320	188,567	9,562	157,650	21,355
8	51,498	294,745	15,168	248,231	31,346
9	77,620	450,386	24,660	378,333	47,393
10	120,676	708,090	36,372	597,994	73,724
11	184,521	1,092,495	58,302	925,321	108,872
12	284,757	1,698,402	85,479	1,444,914	168,009
13	434,618	2,611,459	131,743	2,225,625	254,091
14	680,716	4,116,380	209,853	3,504,148	402,379
15	1,045,880	6,357,099	320,525	5,420,120	616,454

Oblate ellipsoid (parallelepiped shell)#

Oblate spheroid embedded in an inner box with 6 conforming frustums.

Geometry: Semi-axes: a=b=0.5, c=0.25, inner box: 1.0 × 1.0 × 0.5, outer box: 3.0 × 3.0 × 1.5
Extent: [-1.50, 1.50] × [-1.50, 1.50] × [-0.75, 0.75]

Oblate ellipsoid (parallelepiped shell)

Mesh	Nodes	Total tets	body	shell_+x	shell_-x	shell_+y	shell_-y	shell_+z	shell_-z	air
1	1,090	5,117	1,123	478	438	448	443	608	613	966
2	1,312	6,263	1,161	613	561	565	551	856	847	1,109
3	1,836	8,786	1,835	840	810	823	815	1,133	1,162	1,368
4	2,718	13,465	2,801	1,369	1,328	1,330	1,284	1,684	1,714	1,955
5	4,117	20,994	5,045	2,020	1,948	1,919	1,956	2,516	2,460	3,130
6	5,174	26,656	6,893	2,450	2,413	2,454	2,417	3,163	3,122	3,744
7	7,871	41,508	10,975	4,008	3,839	3,886	3,914	4,743	4,722	5,421
8	11,219	60,174	17,245	5,561	5,463	5,497	5,479	6,722	6,671	7,536
9	16,515	90,159	23,777	8,752	8,708	8,778	8,757	10,569	10,487	10,331
10	24,538	136,318	39,896	13,071	12,852	12,861	12,799	15,072	15,080	14,687
11	37,272	210,499	61,390	20,835	20,414	20,265	20,153	23,137	23,146	21,159
12	54,319	309,956	86,430	31,181	31,003	30,775	31,080	35,204	35,438	28,845
13	81,102	467,714	132,531	47,961	47,104	46,654	46,857	53,033	53,307	40,267
14	124,242	725,153	211,251	73,982	72,386	72,793	72,664	81,948	81,108	59,021
15	191,254	1,127,452	340,342	115,667	111,687	112,155	111,488	124,067	124,551	87,495